Problem Statement
Time limit is 3.5 seconds.
Kaede loves maple trees. One day, she found a big maple tree and she described it as an undirected connected graph with N nodes and N-1 edges.
You are given the description in the
There are 2N-1 ways to choose a non-empty subset of nodes. Once we choose a subset of nodes, there is always a unique minimal subtree which contains all nodes in the subset.
Kaede got interested in diameters of these subtrees.
Suppose we iterate over all 2N-1 ways to choose a non-empty subset of nodes, for each of them we construct the unique minimal subtree and then we determine and write down its diameter. Let D be the sum of the 2N-1 values we would write down.
Please help Kaede: calculate and return the value (D modulo 1,000,000,007) for the given tree.
Definition
- Class:
- MapleTree
- Method:
- sum
- Parameters:
- int[], int[]
- Returns:
- int
- Method signature:
- int sum(int[] p, int[] length)
- (be sure your method is public)
Notes
- Given two vertices u, v in a tree, let d(u, v) be the distance between u and v, i.e., the sum of lengths on the unique simple path that connects u and v. The diameter of a tree is the largest out of all values d(u, v).
Constraints
- N will be between 2 and 2000, inclusive.
- p and length will contain exactly N-1 elements each.
- For valid i, p[i] will be between 0 and i, inclusive.
- Each element of length will be between 1 and 10000, inclusive.
Examples
{0, 0, 1, 1, 2}
{1, 2, 1, 1, 2}
Returns: 249
The tree is shown below as ASCII art. Edge lengths are shown using the corresponding number of symbols. 0 / \ 1 \ / \ 2 3 4 \ \ 5 The diameter of this tree is 6. There are 63 different ways in which we can select a non-empty subset of nodes, so the answer is a sum of 63 subtree diameters.
{0, 1, 2, 3}
{10, 10, 10, 10}
Returns: 720
This tree is a line. We can compute the answer as follows: There are 5 non-empty subsets of nodes that produce a subtree of diameter 0. Example subset: {2}. There are 4 non-empty subsets of nodes that produce a subtree of diameter 10. Example subset: {2, 3}. There are 6 non-empty subsets of nodes that produce a subtree of diameter 20. Example subsets: {0, 2} and {1, 2, 3}. There are 8 non-empty subsets of nodes that produce a subtree of diameter 30. Example subset: {0, 1, 3}. There are 8 non-empty subsets of nodes that produce a subtree of diameter 40. Example subset: {0, 1, 2, 3, 4}. Thus, the sum of all 31 diameters is 4*10 + 6*20 + 8*30 + 8*40 = 720.
{0, 0, 0, 0}
{10, 10, 10, 10}
Returns: 480
This tree is a star. Among the 31 subtrees whose diameters we are interested in are five with diameter 0, four with diameter 10, and twenty-two with diameter 20. Thus, the sum of all diameters is 4*10 + 22*20 = 480.
{0}
{1}
Returns: 1
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Returns: 836267973
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Returns: 952816457
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Returns: 647666566
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Returns: 613347951
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Returns: 724395005
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Returns: 136033442
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Returns: 680960844
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Returns: 136930271
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Returns: 155582493
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Returns: 327081513
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Returns: 201835085
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Returns: 705892980
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Returns: 857370777
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Returns: 422367002
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{2,2,1,1,1,1,1,2,1,2,2,2,1,1,2,1,1,1,1,2,2,1,1,2,2,2,2,2,1,1,2,2,2,1,2,1,2,2,1,1,2,2,2,2,2,2,2,1,2,1,1,1,2,1,2,1,1,1,2,2,2,1,1,2,1,1,2,2,2,2,2,1,1,2,2,1,1,2,1,1,2,2,2,1,1,2,2,1,1,1,1,2,1,2,1,1,2,1,1,1,2,2,1,1,2,2,1,1,1,1,1,1,1,1,1,2,1,2,2,1,2,1,2,2,2,1,2,2,2,1,2,2,1,2,1,1,2,2,2,2,2,1,2,1,1,1,2,2,2,1,1,2,2,1,1,2,2,2,1,2,2,2,2,1,1,2,1,1,1,2,1,1,1,1,2,2,1,2,1,2,1,2,2,1,2,2,1,2,1,1,2,1,1,1,2,1,1,1,2,2,2,1,1,2,2,2,2,2,2,1,1,2,2,1,1,1,2,2,2,1,2,1,2,2,1,1,1,2,1,2,1,1,2,2,2,1,2,1,1,2,1,2,2,2,1,2,1,2,1,1,2,1,2,1,2,1,1,1,2,2,1,1,1,1,1,1,2,2,1,2,2,1,1,2,2,2,2,2,2,2,1,1,2,1,1,2,1,2,2,2,1,1,2,2,1,1,2,1,1,2,1,1,1,2,2,1,2,2,1,2,2,1,2,1,1,2,2,2,1,2,1,2,2,1,1,1,2,1,2,2,1,2,2,2,1,1,1,2,2,1,1,2,1,2,2,2,2,2,1,1,1,1,1,2,1,1,2,1,1,2,2,2,1,2,2,2,2,2,2,2,2,2,2,1,2,1,2,2,1,2,1,1,2,1,2,2,1,1,2,1,1,2,1,2,2,1,2,1,1,2,1,1,1,2,1,1,1,2,2,1,2,1,1,1,1,1,1,2,2,2,2,2,1,1,2,1,1,2,2,2,1,2,2,2,1,2,1,1,2,2,2,1,1,2,2,1,2,2,2,2,2,1,1,1,2,1,1,2,2,1,1,2,2,2,2,1,2,1,1,1,2,2,2,2,1,2,2,1,1,2,1,1,1,1,2,1,2,2,1,1,1,2,1,1,1,2,2,1,1,2,1,2,2,2,2,1,1,1,2,1,2,1,1,1,1,2,1,2,1,1,1,2,1,1,1,1,1,1,2,1,2,1,2,2,1,1,1,2,1,2,1,1,2,2,2,2,2,2,1,1,1,2,2,1,2,2,2,1,2,1,1,2,1,2,1,1,2,2,1,2,2,2,1,1,2,2,1,2,2,2,1,1,2,2,2,2,1,1,2,1,1,1,1,2,2,2,2,1,1,2,1,1,2,1,2,1,1,2,1,2,2,2,1,2,1,2,1,2,2,2,1,2,2,1,2,2,2,1,1,2,2,2,1,1,2,2,1,2,2,2,2,2,2,2,2,1,2,1,2,1,2,2,2,1,2,2,2,1,2,2,1,1,1,1,2,1,2,1,1,1,2,1,1,1,1,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,1,2,2,2,1,1,2,1,1,2,2,2,1,2,2,2,1,2,2,2,1,1,1,1,2,1,2,2,1,2,1,2,2,2,1,1,2,1,1,1,1,1,2,2,2,2,2,2,2,2,1,1,1,1,2,2,2,2,1,2,2,1,1,1,2,1,2,1,2,2,2,2,2,1,1,2,2,1,1,2,2,2,2,2,2,2,1,2,2,1,2,1,1,1,2,2,1,1,2,2,1,1,1,2,1,2,2,1,2,1,1,2,2,2,1,1,2,2,1,1,2,2,2,1,1,2,1,2,2,1,1,2,1,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1,2,1,1,2,2,1,2,1,1,1,2,1,1,1,1,1,2,2,1,2,2,2,1,2,2,2,1,1,1,1,2,2,2,2,1,1,1,2,2,2,2,2,1,2,2,2,2,2,1,2,1,2,2,2,2,1,2,2,2,1,2,1,1,1,1,1,1,1,1,1,2,2,1,2,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,2,1,2,1,2,2,1,1,2,2,1,1,1,2,1,1,1,2,2,2,1,1,2,1,1,1,1,1,1,2,1,1,2,1,1,1,2,1,2,1,1,1,2,1,1,2,1,2,2,2,2,1,1,2,2,1,2,2,1,1,1,2,1,2,2,2,2,1,2,2,1,1,2,2,1,1,2,2,2,1,2,2,1,2,2,1,2,2,2,1,1,2,1,1,2,2,1,2,1,1,1,1,1,1,1,2,1,1,1,2,1,2,1,2,1,2,2,1,2,1,2,2,1,2,1,2,2,1,2,1,2,1,1,2,2,2,1,1,1,1,2,1,2,1,1,1,1,2,1,1,1,1,1,2,2,1,2,2,2,1,2,2,1,2,1,1,2,2,2,1,2,1,1,2,2,1,2,2,2,1,2,1,1,2,2,2,2,2,2,1,2,1,2,2,2,1,1,1,1,2,1,1,2,2,2,1,2,2,1,2,2,1,1,1,2,2,2,1,1,1,2,1,1,2,2,2,2,1,2,1,2,2,1,1,1,1,2,2,2,1,2,2,1,2,1,1,1,1,1,2,1,2,1,2,1,1,1,1,2,2,2,2,2,2,2,2,1,2,2,1,2,1,1,2,2,1,2,1,1,2,1,2,2,2,1,2,2,2,2,1,1,1,2,2,1,1,2,2,2,1,2,2,2,2,2,1,1,2,2,2,1,2,1,2,2,2,1,2,2,2,2,2,1,2,1,2,1,2,2,1,1,1,2,1,2,2,1,1,1,2,1,2,1,2,1,2,1,1,2,1,1,2,2,2,1,1,2,1,1,1,2,2,1,1,1,1,1,2,2,2,1,2,2,1,1,1,1,1,2,1,2,1,2,1,1,1,1,1,2,2,2,2,2,2,2,2,1,1,2,1,2,1,1,1,2,1,1,2,2,2,2,2,1,1,2,1,1,2,2,2,1,1,2,2,1,2,2,2,2,2,1,2,1,1,2,2,2,1,1,1,1,2,1,1,1,1,2,1,2,2,1,2,2,2,1,2,2,1,2,2,1,2,2,1,1,2,1,2,1,1,2,2,2,1,2,1,2,2,2,1,1,2,1,1,1,1,1,1,1,2,2,1,1,1,2,1,2,2,2,2,1,1,1,1,1,2,2,2,1,2,2,2,1,2,2,2,2,1,2,1,1,2,1,1,2,1,1,1,1,1,2,1,2,2,1,1,1,1,2,1,1,2,1,1,2,2,2,1,1,2,1,2,1,1,2,1,1,2,1,2,2,2,1,2,1,1,1,2,1,2,1,2,1,1,2,1,1,2,1,2,2,1,1,1,2,2,1,2,1,1,1,2,1,1,1,2,2,1,2,2,2,2,2,1,2,2,1,2,1,1,1,2,1,1,2,2,2,2,1,1,2,2,1,2,2,2,2,2,1,1,2,2,2,2,2,2,1,1,2,1,1,2,1,2,1,2,1,2,1,1,1,1,2,1,2,1,2,1,1,2,2,1,1,1,2,1,1,1,1,2,2,1,2,1,2,2,2,1,1,2,1,1,1,2,1,1,2,1,2,2,2,2,1,2,2,1,2,2,1,1,2,1,1,2,1,1,2,1,2,1,1,2,1,2,1,2,1,2,2,1,1,2,2,1,2,1,2,2,1,1,2,1,2,2,2,1,2,1,2,2,1,2,1,1,2,1,2,2,2,2,2,2,1,2,2,1,2,2,1,1,2,1,2,1,1,1,1,1,2,1,1,2,1,2,1,2,1,1,2,1,1,1,1,1,2,2,2,2,2,1,2,1,1,2,2,2,1,2,2,1,2,1,2,2,2,2,1,1,1,1,1,1,1,2,2,1,1,2,1,1,1,1,1,2,2,1,2,2,2,2,1,2,1,1,2,2,2,2,2,1,1,1,2,2,2,1,1,1,2,2,1,1,2,2,1,2,2,1,2,1,2,1,1,2,2,2,2,1,1,1,1,1,2,1,2,2,1,1,2,1,1,2,2,2,2,2,2,1,2,2,2,2,2,1,1,1,1,2,2,1,1,1,2,2,1,2,1,1,2,1,1,1,2,2,2,1,1,1,1,2,1,1,1,2,1,2,1,1,2,1,2,2,1,1,2,2,1,1,2,2,2,2,1,1,1,1,1,1,1,2,2,1,1,1,1,2,1,2,1,2,1,2,1,1,1,2,1,2,2,2,2,1,1,2,1,1,1,2,1,1,1,2,2,1,2,2,1,1,2,1,1,1,2,2,1,1,2,2,2,2,1,1,2,2,1,1,2,2,2,2,2,1,2,1,1,2,1,2,1,1,1,1,1,1,1,2,1,1,1,2,1,1,1,1,2,1,1,1,2,1,2,1,1,1,2,1,1,2,1,1,1,2,2,1,2,1,1,2}
Returns: 190890400
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{2,1,1,1,1,1,1,2,1,2,1,1,1,2,2,1,2,1,2,2,2,2,1,1,2,2,2,2,1,1,1,2,1,2,1,2,2,1,1,2,2,1,2,1,2,1,2,2,1,1,2,2,1,1,2,1,1,2,2,2,1,2,1,1,1,1,1,1,2,1,1,1,1,1,2,2,2,2,2,2,1,2,2,1,2,2,1,1,1,1,1,1,2,2,2,1,1,1,1,1,2,1,1,1,1,1,1,2,1,2,1,2,1,2,1,1,1,2,1,2,2,1,2,1,1,1,2,2,1,1,1,2,1,2,2,2,2,1,2,1,2,2,1,2,1,2,2,2,2,2,1,1,2,2,1,1,2,1,1,1,1,2,2,2,1,1,2,2,1,2,2,2,2,2,1,2,1,1,1,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2,2,2,1,1,2,1,1,1,2,1,1,2,2,1,1,1,1,2,1,1,2,2,1,1,2,1,2,2,1,1,1,1,1,2,2,1,1,2,1,2,2,2,2,1,2,2,1,2,2,1,2,1,2,1,1,1,1,1,2,1,1,1,2,2,2,2,1,2,2,2,1,2,2,1,1,1,1,2,1,1,1,2,1,2,1,2,1,2,1,2,1,2,2,1,2,2,2,2,1,1,1,2,2,2,2,1,2,1,1,2,2,2,1,1,2,1,2,2,2,2,2,2,1,1,2,2,1,1,2,2,2,2,2,2,2,2,1,2,2,1,2,1,1,1,2,2,1,1,2,1,2,1,1,2,1,1,1,2,1,1,1,2,2,1,2,1,2,1,2,2,2,2,2,1,2,1,2,1,1,2,2,1,1,2,2,1,2,1,1,2,1,1,2,1,1,2,2,1,1,1,1,1,1,2,2,1,2,2,2,1,1,1,2,2,2,2,2,2,2,2,1,2,1,2,1,1,2,2,1,1,1,2,1,2,1,1,1,2,1,1,2,1,2,1,2,1,1,1,2,2,1,1,1,2,2,1,2,2,2,1,1,1,1,2,1,2,2,1,2,2,1,2,1,1,2,1,2,1,2,2,2,1,1,1,1,2,1,2,2,2,1,1,1,2,2,2,1,1,2,1,2,2,1,1,2,1,1,1,1,2,2,2,2,1,1,1,2,1,2,1,1,2,1,1,2,1,2,2,2,2,2,1,2,2,1,2,2,1,1,2,1,1,2,2,2,2,2,2,1,2,1,1,2,2,2,1,1,1,1,1,2,1,1,2,2,1,2,2,2,1,1,1,2,1,1,2,1,1,2,1,2,2,2,2,2,2,1,1,2,1,1,1,2,2,2,2,2,2,1,2,2,1,1,1,1,2,2,2,1,1,1,2,2,2,1,2,2,2,2,2,1,2,2,1,1,1,1,1,1,1,1,2,2,2,1,2,1,1,2,2,1,1,1,2,2,2,2,2,1,2,1,1,1,1,2,2,2,1,1,1,1,2,2,2,1,1,1,1,2,1,2,1,1,2,1,1,1,2,1,2,2,2,2,2,1,1,2,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,1,1,1,2,2,1,2,1,2,1,1,1,1,1,1,2,2,1,2,2,1,2,2,1,1,1,2,2,2,2,1,1,2,2,2,2,1,1,2,2,1,1,1,1,2,1,1,2,1,2,2,1,2,2,1,2,1,1,1,2,1,2,2,1,1,2,1,1,2,2,1,1,1,1,2,1,1,2,2,1,2,1,2,1,2,1,2,2,2,1,1,2,2,1,2,2,1,1,1,2,1,1,2,1,1,2,1,1,1,2,1,1,1,1,2,2,1,1,1,2,2,2,2,2,2,1,1,2,2,1,1,2,1,1,2,2,2,1,1,1,2,2,1,2,1,1,1,2,1,2,1,2,2,1,2,2,2,2,2,2,2,1,1,1,1,2,1,1,2,1,2,1,1,2,2,1,2,2,2,1,1,1,2,1,1,2,2,1,1,1,2,1,2,1,2,1,2,1,2,1,2,2,2,2,2,2,1,1,2,2,2,2,2,1,2,1,1,1,1,1,2,2,1,1,2,1,2,2,2,2,1,1,2,2,1,1,1,1,2,1,2,2,1,2,2,1,2,1,1,1,1,2,1,1,2,2,2,1,1,2,1,2,2,1,2,2,2,1,1,1,1,1,2,1,2,1,2,2,1,2,1,2,2,1,2,2,1,1,2,1,2,2,1,2,2,1,1,1,2,1,2,2,2,1,1,1,1,1,2,2,2,1,2,1,1,1,1,1,1,1,1,2,2,1,2,1,1,1,2,1,1,2,1,2,1,1,2,2,1,1,2,2,1,2,1,1,1,2,2,2,2,1,1,2,2,1,1,1,2,2,1,1,2,2,1,2,1,2,2,2,2,1,1,2,2,1,2,2,1,1,2,2,2,1,1,1,2,2,2,1,1,1,1,2,1,1,1,2,1,2,1,2,2,2,2,1,2,1,2,1,1,1,2,2,2,2,1,1,1,2,1,1,2,2,2,1,2,1,1,2,1,1,2,1,1,2,1,1,1,2,2,1,2,1,1,2,1,1,1,1,1,1,2,2,1,1,2,2,2,1,2,2,1,1,2,2,1,1,2,2,1,1,2,1,1,1,2,1,1,1,2,2,1,2,2,1,2,1,1,2,1,2,1,2,1,1,2,1,1,2,1,1,1,1,2,1,2,1,1,2,1,2,1,1,1,2,2,1,2,2,2,2,2,1,1,2,1,1,1,1,2,2,2,1,1,2,2,2,1,1,2,2,1,1,2,2,1,1,2,1,2,1,1,1,2,1,1,2,1,1,2,2,2,1,2,2,2,1,2,2,2,2,2,2,2,2,2,2,1,1,2,2,2,1,1,2,1,1,1,2,2,2,2,2,1,2,1,2,1,2,2,2,2,1,1,1,2,2,2,2,2,2,2,2,1,2,1,1,2,2,1,1,1,1,2,2,1,1,1,1,1,2,1,2,2,1,1,2,1,2,2,1,2,2,2,1,1,2,2,2,2,1,1,1,2,2,1,2,1,1,2,2,2,1,2,1,1,1,2,1,1,1,2,1,1,2,2,1,1,2,2,1,1,1,1,1,2,2,2,2,2,1,2,1,2,1,1,2,1,1,2,1,1,1,1,1,1,1,2,2,2,1,1,2,1,1,1,2,2,2,1,1,2,1,2,1,2,2,2,2,2,2,1,1,2,2,1,2,1,2,2,1,1,1,2,1,2,1,2,2,2,1,1,2,2,1,2,1,2,2,1,1,1,2,1,2,2,1,2,1,2,2,2,2,2,1,2,2,2,2,1,2,1,2,1,2,2,1,1,1,2,2,1,2,2,2,1,1,1,2,1,1,1,1,2,2,1,2,1,1,1,2,1,1,1,1,2,2,1,1,1,2,2,1,2,2,2,1,1,2,2,1,1,1,2,2,1,1,2,1,1,2,2,1,2,1,2,2,2,1,2,2,1,2,1,1,1,1,1,2,2,2,1,2,2,1,1,2,2,2,1,2,2,1,1,1,2,1,1,2,2,2,2,2,1,1,2,2,1,2,2,1,1,1,2,2,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,2,1,2,1,2,1,1,2,1,2,1,1,2,2,2,1,1,1,1,1,1,1,1,2,2,2,1,1,1,2,1,2,2,1,1,1,1,2,1,2,2,1,1,1,1,2,1,1,1,2,2,2,1,2,1,2,2,1,1,2,2,2,2,2,1,1,2,1,2,2,1,2,2,1,1,1,2,1,1,2,2,1,1,1,1,2,2,1,2,1,1,1,2,1,2,2,1,1,1,2,2,1,1,2,2,1,2,1,1,1,1,1,2,2,2,2,1,1,2,1,2,1,2,1,1,2,1,1,2,2,2,2,2,2,1,2,2,2,1,2,1,1,1,2,2,2,2,1,2,2,1,1,1,2,1,2,1,2,1,1,1,2,2,1,1,1,1,2,2,2,2,2,1,1,2,1,2,2,2,1,1,1,1,2,2,1,2,2,1,1,2,1,2,2,2,1,2,1,1,1,1,2,1,2,1,1,1,2,1,2,1,2,2,2,2,2,2,1,2,2,2,1,1,1,1,2,2,1,1,1,1,1,2,2,1,1,1,2,1,1,2,1,1,1,1,2,2,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,2,2,1,2,2,2,2,2,1,1,2,2,1,2,1,2,2,2,2,2,1,2,1,1,1,1,2,2,2,2,2,1,1,2,2,2,2,2,2,1,2,1,2,1,1,1,2,2,2,1,2,1,2,2,2,2,2,2,2,1,1,1,1,1,1,2,1,2,1,2,1,2,2,2,1,1,1,2,2,2,1,1,2,2,1,1,1,1,1,2,1,2,2,2,2,2,2,1,1,2,1,1,1,2,2,1,2,1,2,1,1}
Returns: 712151429
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{3,3,2,1,1,3,1,2,2,1,3,3,2,3,3,1,1,1,3,1,3,2,3,3,3,1,2,1,1,1,3,2,3,3,1,3,2,1,2,1,2,1,2,1,1,1,3,3,2,3,2,3,2,3,2,3,1,1,3,1,1,3,2,1,1,3,1,1,1,1,2,3,1,2,1,2,2,3,2,1,1,2,3,2,2,3,2,1,2,3,3,1,1,3,1,3,3,1,1,3,3,3,1,3,1,1,2,1,2,1,2,3,2,3,3,3,3,1,2,1,2,1,1,2,2,3,1,2,2,3,3,1,3,3,2,3,2,3,1,2,3,3,1,3,2,2,2,3,1,1,3,2,2,2,2,2,3,1,1,1,2,2,2,3,3,2,1,1,2,3,2,2,2,2,2,2,3,3,1,3,3,1,1,1,2,1,2,2,3,1,2,3,1,1,1,2,3,2,3,3,2,2,2,2,2,1,1,1,1,1,1,1,3,1,3,1,3,2,1,3,1,1,3,2,2,1,2,2,2,1,2,1,3,3,1,1,1,2,1,2,1,2,3,3,2,1,1,2,2,3,1,1,3,3,1,1,3,2,2,3,1,3,3,2,3,2,2,3,3,2,1,1,1,1,1,2,3,3,1,2,2,3,2,1,2,1,3,1,2,3,1,3,3,3,3,2,1,1,3,2,2,2,1,3,1,3,3,3,1,1,1,2,1,1,3,2,2,3,2,1,2,2,2,3,2,3,3,3,2,2,1,2,1,3,3,3,2,3,3,3,3,3,2,2,1,2,3,2,2,2,1,3,2,2,3,3,3,2,3,3,2,3,1,1,2,3,2,3,1,2,2,3,3,1,1,1,3,3,2,2,3,1,1,2,2,2,1,3,3,1,2,2,3,2,3,3,2,3,2,1,2,3,2,2,3,3,1,2,2,1,3,3,3,2,3,1,2,1,3,2,1,1,2,2,3,3,3,3,1,3,2,1,1,3,3,1,2,1,3,3,2,1,3,3,3,3,1,1,3,1,3,2,3,3,3,3,1,1,3,3,1,1,3,3,3,1,3,3,2,1,3,2,1,3,3,1,3,3,2,1,1,1,1,1,1,2,1,1,2,3,1,3,3,2,2,3,3,1,1,1,3,3,3,3,1,1,1,2,2,3,2,3,1,1,1,2,2,1,3,1,1,1,2,1,2,2,3,1,3,3,2,1,2,1,1,3,3,3,3,2,1,1,3,3,3,3,2,1,2,3,2,1,1,1,3,2,2,2,3,1,1,3,3,1,1,1,1,3,2,3,2,3,3,3,1,3,3,3,2,3,3,2,2,3,1,3,2,1,2,3,1,2,3,1,2,2,2,1,3,1,3,2,2,3,3,3,3,1,2,1,3,2,3,3,2,1,2,1,1,2,2,3,2,2,2,3,3,1,1,1,3,1,3,3,3,1,2,2,1,1,2,1,1,2,1,3,1,1,3,1,1,1,2,3,3,3,1,3,1,2,1,1,1,2,2,3,1,2,3,2,2,3,3,1,3,1,3,3,1,1,1,2,1,3,2,2,3,1,3,2,3,3,3,1,3,1,3,1,1,2,3,1,2,1,1,2,1,1,3,3,1,1,2,2,3,2,2,3,2,3,3,3,3,2,3,2,3,2,3,2,2,1,1,3,2,1,3,2,1,3,1,2,2,3,1,1,1,2,1,2,2,1,1,2,3,2,2,1,2,3,2,1,1,2,2,3,1,1,1,2,1,1,1,2,1,1,2,3,1,2,3,3,1,3,3,1,2,2,3,2,2,1,1,3,1,1,1,1,2,2,3,2,3,2,3,2,2,1,3,2,3,3,3,3,2,1,3,1,3,2,3,3,2,3,2,2,1,3,2,3,2,1,3,2,2,1,2,2,3,2,2,3,1,2,2,2,3,1,3,2,3,3,2,3,3,2,2,3,3,2,3,3,3,3,3,2,2,1,1,1,2,1,1,1,3,2,3,3,3,1,2,3,1,2,1,2,3,1,2,1,1,3,3,1,3,3,3,2,1,2,1,1,2,2,1,3,1,1,2,3,1,2,3,2,2,3,1,2,3,3,2,2,3,1,2,2,3,1,3,1,3,2,1,3,2,1,1,1,3,2,3,3,3,3,3,2,2,2,3,3,1,1,2,3,1,2,3,3,1,2,2,2,2,1,3,3,1,2,1,1,2,2,1,3,2,3,3,1,2,1,2,3,1,3,1,1,1,2,2,3,1,2,3,2,3,1,2,1,3,1,2,1,2,3,2,3,3,2,1,3,1,1,2,2,2,3,2,3,2,1,1,1,3,3,1,3,3,1,2,1,3,2,1,3,1,2,2,3,3,2,2,3,3,1,1,1,2,2,1,1,1,3,3,2,2,1,1,2,2,2,1,1,2,1,2,1,1,3,2,1,3,1,2,3,3,2,1,1,3,1,3,1,2,1,2,3,3,2,1,3,1,1,3,1,3,2,1,1,3,1,2,3,1,3,2,2,1,3,1,1,3,1,3,1,2,1,2,1,1,3,3,2,2,1,3,3,2,1,2,2,2,3,2,3,1,2,3,1,3,3,2,2,3,2,3,2,1,1,1,3,1,1,1,3,1,2,2,3,3,1,3,2,3,3,2,2,2,1,1,2,3,2,1,2,1,1,2,1,1,1,1,3,2,3,3,1,3,3,1,3,2,1,3,1,1,2,2,3,1,1,3,3,1,1,2,3,3,2,1,3,2,2,3,2,2,1,3,2,3,3,2,2,2,1,2,2,3,1,2,3,3,1,3,1,3,2,2,1,3,2,3,1,2,1,3,3,2,1,2,2,1,3,1,1,3,3,1,3,3,3,1,2,2,1,1,2,1,2,3,3,2,1,2,2,1,1,3,3,1,1,3,2,1,1,2,1,3,1,1,3,1,3,2,1,1,1,1,3,2,1,3,1,2,3,1,3,1,2,2,3,1,3,2,3,1,1,3,1,2,1,1,3,3,3,3,2,1,1,1,1,2,1,2,1,2,3,2,2,2,3,1,3,2,1,2,1,1,3,2,1,2,3,2,2,3,3,2,3,1,3,2,1,3,3,3,3,3,2,1,2,1,1,2,1,1,1,1,1,1,1,2,3,1,1,1,3,2,2,1,3,2,1,2,1,2,1,1,2,1,2,2,1,3,1,1,1,3,3,1,2,3,2,3,2,3,2,3,1,1,3,1,1,2,1,1,3,3,2,2,2,1,2,2,1,3,1,1,2,1,1,1,2,2,3,2,2,2,2,2,1,1,2,2,2,1,2,2,1,2,3,2,1,3,1,3,2,2,3,1,2,3,2,1,1,2,1,3,1,3,3,1,3,2,3,1,3,2,2,2,1,1,1,2,2,1,1,3,3,3,2,1,3,1,1,3,2,1,3,3,2,3,2,2,2,1,2,1,1,3,1,2,2,3,1,1,1,1,1,3,3,1,2,3,2,2,3,1,1,1,1,1,2,3,3,3,3,3,3,1,3,1,3,2,1,3,1,3,2,3,2,1,2,2,1,2,1,3,2,2,2,1,1,3,2,1,2,2,2,2,3,3,3,2,1,2,2,2,2,1,1,1,2,2,2,1,3,1,2,1,2,1,3,3,2,3,2,1,1,3,1,3,1,2,2,2,1,1,3,1,1,1,3,3,3,2,1,1,3,1,1,1,3,1,1,1,1,3,3,1,3,2,1,3,2,1,3,1,3,2,2,2,2,1,1,1,3,3,2,1,3,3,3,3,2,2,1,3,2,3,3,2,3,3,1,1,2,2,1,3,3,2,3,1,3,1,2,2,3,1,1,3,1,1,2,1,1,2,2,3,3,2,1,1,1,2,3,2,3,3,1,2,2,3,3,1,2,1,3,3,3,2,2,1,2,1,1,1,1,1,1,3,1,3,2,3,1,3,2,3,3,3,2,3,1,3,3,2,1,3,1,2,3,1,2,1,1,1,2,3,2,1,2,1,2,1,2,3,1,2,3,3,2,1,3,3,2,1,1,3,3,3,2,1,2,1,2,1,2,2,1,3,2,2,1,2,1,1,2,3,2,2,3,1,2,2,2,3,1,2,1,3,1,1,3,1,3,3,3,3,3,3,1,3,1,1,2,1,1,3,3,2,3,1,2,3,2,1,3,1,1,3,3,2,1,2,2,1,1,1,2,1,2,2,2,1,2,3,3,2,3,1,1,1,1,1,1,1,3,2,2,3,1,2,2,2,1,3,3,1,2,2,2,1,2,1,1,3,2,1,2,2,1,2,2,1,2,3,3,1,3,2,3,1,2,3,1,2,1,1,1,2,2,2,1,1,3,2,1,2,1,1,3,2,3,2,2,1,2,3,2,3,3,3,1,1,1,3,3,3,2,1,2,2,2,2,2,1,1,3,2,2,2,3,2,2,2,2,2,2,3,2,1,3,2,1,2,1,1,3,1,1,1,2,1,1,1,3,2,2,3,1,3,1,1,2,2,3,3,3,3,2,3,1,3,3,2,3,1,1}
Returns: 851311305
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{1,3,2,2,1,2,1,1,1,3,1,2,1,3,1,2,3,3,1,2,1,1,3,1,2,3,3,1,2,2,3,3,3,1,2,2,1,3,3,3,2,3,1,2,2,1,1,2,3,3,3,3,2,1,2,3,2,3,2,2,2,2,3,2,2,1,3,2,2,1,1,2,1,2,3,3,2,1,1,2,1,3,3,1,3,1,2,2,3,1,3,2,1,1,2,3,1,3,2,2,1,2,2,1,2,3,2,2,2,2,3,2,2,3,3,3,2,3,1,2,1,2,3,1,1,3,1,2,1,3,3,1,2,2,3,3,3,1,1,3,2,1,1,2,1,2,1,1,3,2,3,2,1,1,1,3,3,1,1,3,3,1,1,1,2,2,2,2,2,3,2,2,3,3,2,3,2,1,2,3,3,1,2,2,3,2,1,3,2,3,1,3,1,1,2,1,2,1,1,3,3,2,1,2,3,2,3,2,1,2,3,3,1,1,2,3,2,2,2,1,1,3,3,2,2,1,1,2,3,3,1,2,1,2,2,3,2,3,2,2,1,2,2,1,2,1,1,2,1,1,1,2,2,3,1,1,1,2,2,2,2,2,2,2,1,2,1,1,2,2,1,3,3,3,3,2,3,3,3,1,1,1,1,3,1,3,2,2,2,3,2,3,2,1,1,3,3,2,3,3,2,3,3,3,3,2,1,2,2,2,3,1,1,3,3,1,1,2,2,3,1,2,1,1,1,3,1,1,1,1,2,2,1,2,1,2,3,2,1,3,2,2,2,1,2,1,3,3,1,3,1,3,2,2,1,2,2,2,3,1,3,1,1,1,2,1,3,3,1,3,3,2,1,2,1,3,1,1,2,1,1,3,3,1,3,3,3,2,3,3,1,1,3,3,3,1,2,3,3,3,2,3,2,3,3,3,2,1,3,1,1,1,2,2,2,1,3,2,3,1,1,1,3,2,1,2,1,3,2,2,3,3,2,1,3,2,1,2,2,3,3,1,2,3,2,1,3,2,1,1,3,1,3,3,2,1,2,3,2,3,1,3,2,2,1,1,2,3,2,1,1,3,2,2,3,1,1,2,1,2,2,2,1,3,2,1,1,2,3,2,3,1,1,1,1,3,3,2,2,1,2,1,2,3,3,1,2,3,2,3,3,1,2,2,2,2,3,2,1,3,1,1,1,3,1,3,1,1,2,2,3,2,1,3,3,3,3,2,3,1,1,3,3,1,2,1,1,2,3,1,3,1,2,2,3,1,3,1,2,2,2,3,2,3,2,1,3,2,1,2,3,1,2,1,1,2,3,1,1,3,1,2,3,3,1,2,3,2,3,2,3,3,1,2,3,3,3,2,3,2,1,2,2,3,3,1,3,1,1,1,2,1,1,2,1,3,2,2,2,2,1,1,2,2,1,3,1,3,3,1,2,2,3,1,2,3,1,1,3,2,1,1,1,1,3,2,2,2,1,3,3,1,2,3,3,1,3,1,3,2,3,2,3,1,3,2,3,1,3,1,1,1,3,1,2,1,3,1,3,3,1,3,3,2,3,2,3,2,2,1,2,2,2,2,3,3,2,2,2,3,1,1,3,1,2,1,1,3,3,2,2,1,1,3,1,2,2,1,1,1,3,3,2,3,2,1,3,3,3,3,2,2,3,3,3,3,2,2,3,3,3,2,1,3,2,1,3,2,3,1,1,2,2,1,2,3,1,2,3,1,3,1,2,1,1,1,3,1,2,2,3,3,3,2,1,3,2,1,2,2,1,1,1,3,3,2,3,1,2,3,3,1,2,2,3,3,2,2,1,1,3,3,1,3,2,3,1,2,3,3,3,1,1,3,3,3,2,2,3,2,1,3,3,3,1,3,2,2,2,2,2,3,1,2,3,1,3,2,1,1,1,3,2,3,3,1,1,1,3,1,3,1,1,2,2,3,1,1,3,1,1,1,3,3,1,1,1,1,3,3,1,1,3,2,3,3,2,2,2,2,1,3,3,1,3,3,2,2,3,1,1,3,2,1,1,1,1,1,3,3,1,1,3,2,1,3,1,2,3,3,3,1,1,2,3,2,3,3,3,1,2,2,2,1,3,3,3,1,1,2,2,2,3,2,1,1,2,3,1,2,3,2,2,3,2,3,1,2,3,3,2,1,1,3,3,3,1,3,1,1,1,2,3,3,3,2,2,2,1,2,1,2,1,2,2,1,1,3,1,3,2,2,3,2,1,3,2,1,2,3,2,2,2,3,3,1,2,1,3,1,2,3,2,3,1,3,3,1,3,1,2,2,2,3,3,3,3,2,1,1,2,3,3,3,1,1,3,3,3,1,1,3,1,3,1,3,2,1,3,2,2,2,1,2,3,2,3,3,1,2,2,1,1,3,1,1,2,2,1,2,3,3,2,2,3,2,3,3,1,2,2,2,2,1,1,3,2,1,3,3,3,1,3,1,1,1,3,2,1,1,3,1,3,3,3,1,1,1,2,2,2,2,2,3,1,2,3,3,1,3,3,3,2,1,1,2,1,1,2,1,3,3,3,1,2,2,1,2,1,1,1,1,2,1,3,1,3,2,2,1,2,3,1,2,1,2,1,2,1,1,2,2,1,2,2,1,1,2,1,3,2,3,2,3,2,2,1,1,2,3,1,1,1,1,2,3,3,1,1,1,2,2,3,2,3,3,3,2,2,1,1,2,1,3,1,2,3,3,1,3,1,1,1,1,3,2,3,1,2,1,2,3,3,1,1,1,2,2,1,3,1,1,3,2,2,1,3,1,2,1,1,1,3,3,1,2,1,1,1,2,1,1,2,3,3,2,2,2,1,3,1,2,3,3,3,1,3,3,2,1,1,2,1,3,3,3,3,2,3,3,2,3,3,1,2,1,3,3,3,2,1,2,3,3,1,2,1,2,3,3,1,2,2,3,1,3,1,3,1,1,1,3,3,2,3,1,1,3,1,2,1,3,3,2,2,1,1,3,1,3,2,3,3,3,2,3,2,1,2,2,2,3,3,3,1,2,3,2,2,2,2,2,2,3,1,3,2,1,3,3,2,1,1,2,1,2,3,1,3,1,1,1,3,1,3,1,1,3,2,3,1,3,2,1,2,3,3,1,3,3,2,3,1,2,3,1,2,2,1,2,2,3,3,2,2,2,1,3,1,2,3,2,1,3,1,2,1,1,3,2,1,3,3,1,2,2,1,3,2,3,2,1,3,2,1,3,2,3,2,3,3,3,3,1,2,1,3,1,2,1,3,3,2,1,2,1,1,3,1,2,1,3,1,2,1,2,3,1,2,1,1,1,2,3,1,3,2,3,3,3,1,3,1,2,3,2,1,3,2,3,1,1,2,3,1,3,2,3,3,1,3,3,3,3,3,2,2,3,1,1,1,1,1,3,1,1,2,3,2,3,2,1,3,1,2,3,3,1,1,1,3,2,2,3,2,1,2,3,3,2,1,2,3,2,2,2,1,2,2,3,2,3,2,1,2,2,1,2,3,1,1,1,3,2,1,3,1,2,1,2,3,3,2,1,2,3,3,2,1,1,1,3,1,1,1,3,1,1,1,1,2,3,1,2,3,2,2,3,2,3,3,2,3,1,1,2,1,1,2,3,3,3,1,1,2,1,3,1,1,1,3,2,3,1,2,1,1,2,3,3,2,1,1,1,2,3,3,3,3,2,3,1,3,2,2,3,2,2,1,3,1,3,3,3,3,3,1,3,3,3,2,1,2,2,2,3,1,1,3,3,1,2,1,2,2,3,2,2,2,3,3,2,3,1,3,3,2,2,2,1,2,2,2,1,3,2,3,2,1,3,3,3,3,1,3,2,3,1,2,1,3,2,2,3,2,1,1,1,2,1,3,3,3,3,1,2,1,1,2,2,3,2,2,1,2,1,1,1,1,3,3,3,1,3,1,1,1,1,2,3,1,3,1,2,3,3,2,2,3,2,2,2,2,3,3,3,2,3,1,3,3,1,1,2,2,3,3,3,2,1,1,2,1,2,3,1,2,1,2,1,3,2,3,1,2,1,2,2,3,2,1,2,1,1,2,3,1,3,3,1,3,2,3,1,1,1,3,1,2,3,2,2,3,2,1,2,1,1,2,3,1,2,1,1,1,2,2,3,3,2,3,1,3,3,2,1,1,2,2,1,3,3,3,2,2,3,3,3,1,3,3,1,1,1,2,2,2,1,1,3,3,3,2,1,2,2,3,1,3,1,1,1,2,3,1,1,1,2,3,1,3,2,2,3,2,1,2,1,3,1,2,3,1,2,2,2,2,1,3,1,3,1,2,2,3,2,2,1,1,2,1,1,1,1,3,3,3,3,1,1,3,1,2,3,1,3,3,3,2,1,2,1,2,1,3,3,1,2,1,1,1,1,3,2,1,2,2,3,1,1,2,2,3,2,1,2,3,3,1,1,1,3,1,3,1,1,2,1,2,3,2,3,3,3,3,3,1,3,1,3,3,3,1,2,3,3,1,2,3}
Returns: 443863104
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{1,3,3,3,2,1,1,3,2,3,2,3,3,1,1,2,3,1,2,3,3,3,1,2,2,3,2,2,3,3,1,3,2,3,1,1,2,3,3,1,3,2,2,1,1,2,2,1,2,1,2,1,2,3,3,3,3,3,2,3,1,2,3,2,3,2,3,1,1,1,2,2,1,1,2,2,1,2,1,1,3,1,3,2,1,3,3,1,2,1,2,3,2,3,1,3,3,1,1,1,1,1,1,2,1,1,2,3,1,1,1,3,2,2,2,1,1,2,3,2,1,2,2,1,1,2,3,1,1,2,3,3,2,1,3,3,1,1,3,1,2,2,3,1,1,3,1,1,1,1,3,3,1,3,2,1,3,3,2,2,2,1,3,1,1,1,2,1,3,2,3,3,3,1,3,2,2,2,3,3,2,1,3,1,3,3,2,1,2,3,2,1,3,2,2,1,1,1,3,3,2,2,3,3,3,2,2,3,1,3,2,1,3,3,2,3,3,1,2,3,3,3,3,2,3,2,3,2,2,3,2,2,1,2,3,1,2,1,3,3,3,1,2,3,1,3,1,1,2,1,3,2,1,1,2,2,2,1,2,3,2,3,1,1,3,3,1,1,1,3,1,2,3,1,2,3,3,1,3,1,3,3,1,3,3,2,2,3,3,2,1,2,3,3,2,1,3,2,1,1,3,1,1,1,2,2,1,2,2,1,3,1,3,3,3,2,2,2,3,1,1,2,3,3,2,2,3,1,2,3,1,2,3,1,1,3,2,1,3,3,2,1,1,3,1,1,2,1,2,2,2,2,2,1,2,3,1,2,1,1,2,1,1,2,2,2,2,3,1,3,3,1,1,3,3,3,1,1,2,1,2,2,3,1,1,3,3,3,1,3,2,3,1,2,3,1,3,1,3,1,1,2,2,3,3,1,1,2,2,1,2,3,2,1,2,3,1,2,1,3,1,3,3,1,1,1,2,1,1,2,3,1,1,3,3,1,3,3,2,3,3,3,2,2,3,2,2,2,1,1,3,2,3,1,2,3,1,1,2,1,3,2,3,1,2,2,3,2,3,2,3,3,3,1,3,2,1,2,3,1,2,3,3,2,2,3,2,1,3,1,2,3,2,1,2,3,1,3,1,2,1,1,3,2,3,1,1,3,1,2,3,1,3,1,3,3,2,2,1,1,1,1,1,2,1,2,1,2,1,2,1,2,2,1,3,1,3,3,2,2,2,3,2,3,1,1,3,3,2,2,1,3,2,1,3,2,3,1,1,3,3,1,3,3,2,3,2,3,1,2,1,1,2,1,3,2,2,1,3,3,3,2,2,3,3,3,3,3,2,3,2,1,3,3,2,3,3,1,1,1,1,1,1,3,2,3,3,2,3,1,3,3,1,2,3,3,1,3,1,1,2,3,1,2,3,3,3,1,3,1,3,3,2,1,1,1,2,1,3,2,2,3,3,1,1,3,3,2,3,1,3,1,2,3,2,2,2,1,1,1,1,1,2,1,3,1,2,2,1,2,1,2,1,1,1,2,1,2,3,2,2,2,2,2,3,1,3,2,3,3,2,1,1,1,1,1,3,1,3,2,3,2,3,2,3,3,1,3,1,1,2,1,1,1,3,2,2,1,2,1,1,3,1,1,2,2,2,3,2,3,2,2,2,1,3,2,1,1,1,3,2,2,2,1,3,3,1,1,3,3,1,1,3,3,2,3,3,2,3,2,3,1,3,3,1,2,3,2,1,1,3,1,1,3,3,2,3,2,2,1,1,2,2,2,1,2,3,1,1,1,1,1,2,1,1,3,3,1,3,1,1,2,3,3,3,3,1,3,2,1,3,3,1,1,3,3,2,3,2,2,2,1,1,2,1,3,1,2,3,3,3,2,2,3,2,2,2,3,1,1,3,3,2,1,3,2,2,1,1,1,1,1,3,3,2,2,3,2,1,2,3,1,1,3,2,1,2,2,1,1,1,3,2,3,1,2,1,1,3,2,3,3,2,2,2,2,1,1,3,3,3,3,3,2,1,1,3,3,2,3,1,1,1,1,1,3,2,2,3,1,1,1,3,3,3,2,2,3,2,1,2,2,2,3,3,3,2,2,1,3,1,1,1,3,2,2,1,3,3,3,1,1,3,1,2,3,1,1,1,2,3,2,2,1,1,2,2,1,2,3,2,3,2,2,1,3,3,3,3,1,2,1,2,2,2,3,3,2,3,3,3,3,2,3,1,1,1,1,2,2,3,3,2,2,1,2,3,1,2,1,3,2,3,3,2,2,3,3,1,2,2,2,3,3,2,3,3,2,1,3,3,2,3,2,3,1,2,2,1,2,3,2,3,3,2,2,2,1,3,3,1,3,2,1,1,1,3,2,2,2,1,2,3,3,3,2,1,3,3,1,2,1,3,1,2,1,1,2,3,3,1,2,3,2,3,1,1,3,3,2,1,1,1,1,3,2,1,3,3,2,3,3,2,3,1,3,3,2,3,1,3,1,1,2,1,2,2,3,1,2,2,2,3,1,1,1,1,1,1,1,1,2,1,2,3,1,1,1,3,1,2,2,3,3,2,1,1,2,2,3,1,2,2,3,1,3,2,2,3,2,1,2,2,3,3,1,2,1,3,2,3,1,3,1,2,2,2,3,2,2,2,1,1,1,1,1,2,1,3,3,2,3,1,2,2,2,3,2,2,3,2,3,1,3,3,2,1,2,1,3,1,3,1,1,1,3,1,2,2,2,1,1,1,3,3,3,1,3,3,2,2,2,3,3,3,2,2,3,2,2,2,2,2,2,2,1,3,1,1,2,1,2,3,2,1,3,2,3,3,1,2,1,2,1,3,2,2,3,2,2,2,1,3,1,3,3,3,1,1,2,3,1,1,1,1,1,2,1,2,3,3,1,1,2,2,3,2,3,1,2,1,3,2,3,2,2,1,1,3,2,1,1,3,3,3,3,3,2,3,2,3,2,1,2,2,3,2,1,1,2,3,2,2,2,3,2,1,1,3,2,2,2,3,3,1,3,3,1,2,3,1,2,3,2,1,2,1,2,2,1,3,2,1,1,3,2,1,1,1,1,2,2,1,3,3,2,3,2,1,2,1,1,2,2,3,3,2,1,2,2,2,1,2,1,1,1,1,1,1,1,2,3,2,2,2,2,2,1,1,3,3,2,1,2,1,3,3,2,2,1,3,2,1,1,1,3,2,1,1,3,3,2,2,1,1,2,1,1,3,3,1,2,2,3,2,2,3,2,3,2,2,2,1,3,3,2,1,2,1,1,3,2,3,1,3,3,2,1,3,2,2,3,2,1,3,1,2,2,1,1,3,1,1,3,2,2,3,1,2,2,3,2,3,2,2,3,3,1,1,1,3,2,3,2,2,2,1,3,3,3,1,1,2,2,3,1,3,3,1,2,3,3,3,3,3,2,3,1,2,1,3,3,1,2,1,3,1,1,2,3,3,3,3,3,1,2,3,3,1,2,1,2,2,3,1,2,1,1,2,2,1,1,2,2,1,1,1,2,1,2,2,2,2,1,2,3,1,3,1,3,2,3,1,2,1,1,2,2,2,3,3,2,3,3,3,2,2,1,3,2,3,1,1,3,1,3,1,2,2,3,2,3,3,3,2,3,2,2,2,1,1,3,1,1,1,2,3,2,1,3,2,2,1,3,1,2,1,2,1,2,3,2,3,2,3,1,3,1,3,1,2,3,1,3,3,2,3,2,2,2,3,1,1,3,3,2,1,1,3,1,1,2,2,1,3,1,1,2,2,3,1,2,2,3,1,3,2,1,2,2,3,1,2,3,2,3,3,3,3,2,2,3,3,3,1,2,3,1,1,2,2,3,2,3,2,2,3,2,1,1,2,1,1,2,2,3,2,3,1,2,3,2,3,3,3,1,3,1,2,3,2,2,2,2,3,3,2,3,3,3,1,2,2,1,3,3,2,2,1,2,3,3,3,2,1,3,1,2,3,1,3,1,3,2,1,2,3,2,2,1,3,1,1,2,3,3,2,1,2,3,2,3,2,1,3,1,3,1,2,2,1,2,3,2,2,3,1,3,2,2,2,2,3,3,2,3,2,2,3,3,1,3,1,1,1,1,1,3,3,2,2,3,3,3,2,2,1,2,3,2,1,2,3,2,2,3,1,1,1,2,3,2,3,3,1,1,1,2,3,1,3,2,3,1,3,3,2,1,2,3,1,2,3,1,2,1,3,2,1,3,1,1,2,2,1,3,1,3,3,3,3,1,3,3,1,1,3,1,3,1,2,3,1,1,2,2,3,1,1,3,1,3,3,1,3,3,3,2,3,3,3,1,1,3,3,2,3,1,3,1,2,2,1,1,3,1,1,2,1,1,1,2,3,3,3,1,2,1,2,2,3,3,1,1,2,3,3,2,2,3,2,2,1,1,1,3,2,2,1,2,3,2,3,3,1,2,2,3,2,3,1,3,1,3,3,2,1,2,3,3,2,1,2,3,2,1,1,3,2,2,2,3,3,2,1,1,2,2,1}
Returns: 180720839
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{1,1,2,2,1,2,2,1,3,2,3,1,3,2,3,3,1,1,2,2,3,1,1,2,3,2,1,1,2,3,2,2,1,3,1,1,1,3,2,1,2,1,3,1,2,2,2,3,2,1,2,1,1,2,1,3,1,2,3,3,1,1,3,3,3,3,2,2,2,3,1,1,2,1,1,1,3,1,1,1,1,2,3,2,3,2,1,1,1,3,3,3,1,2,3,3,3,2,2,1,3,2,3,1,2,3,2,3,2,1,2,1,1,1,2,2,2,2,2,2,3,1,3,1,1,1,1,1,1,3,2,3,2,3,3,2,3,3,3,3,1,2,2,2,1,1,1,2,2,2,1,2,2,1,1,2,2,1,2,2,3,1,2,2,1,1,3,2,3,1,2,3,3,3,2,3,1,1,2,1,1,2,3,1,3,3,2,3,2,2,3,3,2,3,2,3,2,3,2,1,1,2,3,2,2,3,1,1,3,2,1,3,1,3,2,2,3,1,2,3,2,3,3,2,2,1,1,3,1,3,3,1,3,2,2,3,2,2,1,1,1,1,3,1,1,1,1,2,3,1,2,3,3,2,2,1,3,2,3,1,3,3,1,3,3,3,1,3,2,1,1,3,3,3,1,3,3,2,3,3,2,1,1,3,3,1,2,1,2,3,2,3,1,1,1,1,1,3,3,3,2,3,2,2,3,3,1,3,1,1,1,3,1,3,3,1,3,1,2,1,3,3,1,2,3,2,1,1,1,2,1,2,1,3,1,3,2,3,3,2,2,2,1,3,2,1,2,2,1,2,2,1,3,1,1,3,1,3,3,1,1,1,1,2,1,2,2,3,1,1,2,1,1,2,1,3,1,1,2,2,1,1,3,2,2,2,2,3,2,3,2,2,1,3,2,1,1,3,3,3,2,3,1,2,2,3,1,3,2,1,1,1,1,1,2,2,2,2,2,1,1,2,2,2,3,2,2,3,2,3,3,3,3,2,2,1,3,3,3,2,1,3,1,2,1,1,2,1,1,3,2,1,3,3,3,2,1,1,1,2,1,1,3,3,3,1,1,3,3,2,1,2,1,2,1,3,3,2,2,1,3,2,2,2,1,2,2,1,2,2,2,3,1,1,3,3,3,3,3,3,2,3,1,1,1,1,1,3,3,1,1,2,3,1,2,2,2,3,2,2,3,2,3,2,3,2,2,3,1,2,3,2,3,3,3,2,2,2,3,3,3,2,3,2,2,3,1,3,3,2,1,2,1,3,2,2,2,2,3,3,3,1,3,2,1,3,2,1,2,2,3,2,3,1,2,3,2,3,2,2,3,1,1,2,2,3,2,3,1,1,1,1,2,3,2,2,3,1,3,3,1,2,2,1,2,3,3,3,1,3,2,1,1,1,2,3,2,2,3,1,2,1,2,2,1,2,2,1,3,1,2,1,3,1,3,2,2,3,3,2,1,1,1,1,2,2,1,3,3,3,2,1,3,2,1,3,2,1,2,2,2,3,3,3,2,2,1,2,2,2,1,1,2,3,3,3,3,1,2,2,1,2,3,2,1,3,2,3,3,2,3,1,1,2,1,1,2,1,3,1,1,3,2,2,3,1,3,1,2,2,3,1,3,2,1,2,1,1,3,1,2,2,3,2,3,1,1,3,1,2,2,3,2,2,3,2,1,1,2,2,3,3,3,2,3,3,1,2,1,3,1,3,3,3,1,3,1,2,3,2,1,3,3,2,1,2,2,2,2,2,2,1,3,3,1,2,3,2,3,2,2,1,2,3,3,3,2,3,1,1,2,2,1,2,1,2,2,3,2,1,2,2,2,3,3,2,1,3,3,1,3,3,2,3,2,3,2,2,3,2,3,2,2,2,3,2,1,1,1,2,3,2,3,2,3,2,1,1,2,2,2,3,1,1,1,1,3,1,3,2,3,3,2,1,2,2,3,1,2,1,3,2,2,1,1,2,3,1,3,2,3,3,2,2,2,3,1,2,1,2,1,3,2,3,2,2,3,1,1,3,1,2,3,3,3,1,2,1,2,1,2,2,3,1,3,3,1,2,1,1,2,1,3,2,2,2,3,3,3,2,3,1,2,2,1,1,1,1,1,2,2,3,2,3,2,3,1,3,3,3,1,3,2,2,3,1,2,3,2,1,1,3,1,3,3,3,3,2,3,1,1,1,3,2,1,3,2,3,1,2,3,3,2,2,3,1,1,1,3,1,2,3,1,1,3,2,3,3,3,1,2,2,2,1,3,2,1,2,3,2,3,3,3,1,1,1,3,3,3,3,2,2,2,2,2,3,2,1,2,1,2,1,3,2,2,2,3,3,3,2,3,2,2,2,1,2,2,2,1,1,3,3,3,3,2,1,1,1,1,3,3,2,3,3,3,1,3,2,1,1,2,1,1,1,1,2,3,3,2,3,2,3,2,1,2,2,2,3,1,2,2,2,2,1,2,1,3,2,3,3,1,2,3,3,3,1,2,2,1,2,3,3,2,3,3,3,2,3,3,2,1,1,3,2,3,3,3,1,3,1,3,3,1,3,1,1,3,1,1,2,1,2,3,3,1,2,1,1,3,1,1,1,1,3,2,1,2,2,2,3,3,2,1,2,1,1,1,1,1,2,2,2,1,1,1,3,1,1,3,2,2,2,1,2,1,2,3,1,2,3,1,2,3,1,1,1,2,3,3,1,1,1,1,1,2,2,2,2,2,1,1,2,2,1,2,2,1,3,1,3,1,2,3,3,1,1,3,1,2,1,1,2,1,3,2,2,2,1,1,3,2,1,1,3,3,3,3,3,2,1,1,3,1,2,1,3,3,3,3,2,1,1,3,1,1,2,3,1,3,3,2,3,2,2,1,3,1,2,1,1,2,2,1,2,3,3,1,3,3,2,3,1,1,1,3,2,2,3,2,2,1,1,1,1,2,1,3,2,3,3,1,1,1,3,2,1,3,2,1,1,3,3,3,2,3,1,3,2,2,1,3,2,1,2,3,1,2,2,2,2,2,3,2,2,2,1,1,1,3,2,2,3,3,2,2,2,2,2,3,2,3,3,3,2,2,1,3,1,1,3,1,3,3,3,2,1,2,3,3,2,3,3,1,2,1,2,3,2,3,3,2,2,1,2,2,1,3,1,2,3,3,3,1,3,1,3,1,1,3,2,1,3,3,1,3,3,1,2,2,3,3,3,2,2,3,2,2,3,2,3,3,2,1,1,2,2,1,2,2,1,3,2,1,3,3,1,2,1,1,2,3,2,1,2,2,1,1,1,2,2,1,1,3,3,2,2,3,2,2,3,2,1,2,1,2,2,1,2,1,2,2,2,3,3,3,1,2,2,3,3,1,3,2,1,1,3,3,2,2,1,3,3,1,3,1,2,3,2,2,1,1,1,3,1,1,2,1,1,1,1,2,1,3,1,3,2,1,1,3,2,1,3,1,3,1,1,1,1,3,1,1,3,1,2,1,1,1,3,2,2,2,3,1,2,1,1,3,3,3,2,1,3,2,1,2,2,2,2,2,2,1,1,2,1,1,2,1,2,3,1,2,3,3,1,3,2,2,1,3,3,3,3,1,2,2,3,3,3,1,2,1,3,3,1,3,3,1,2,1,2,1,3,2,2,3,1,1,3,2,3,1,3,3,2,3,1,2,3,3,2,2,2,1,3,3,1,2,1,2,3,2,1,1,2,3,3,2,3,1,1,3,3,2,3,2,1,1,2,1,1,1,1,2,2,2,3,3,1,2,3,2,3,3,3,3,1,2,3,1,1,1,2,3,2,3,1,2,3,3,3,3,3,3,3,2,3,2,3,2,3,2,1,3,1,3,1,1,3,2,2,2,2,2,1,1,1,1,1,1,2,3,3,3,3,3,3,3,1,1,1,2,3,2,2,1,3,2,2,1,1,1,1,1,3,2,1,3,3,2,3,2,1,3,2,2,1,1,1,2,2,2,2,3,2,1,1,2,3,3,3,2,3,2,1,2,1,2,2,3,1,2,3,3,2,1,1,2,1,1,3,2,1,3,3,1,1,3,2,2,1,1,1,3,1,2,1,2,3,1,2,2,2,3,2,1,1,2,3,3,2,3,3,2,1,3,1,2,2,1,3,2,2,2,3,2,1,3,3,2,3,2,1,1,3,3,3,1,3,2,3,2,1,2,3,1,1,3,2,3,1,3,3,3,2,1,2,2,3,3,2,2,3,3,2,1,3,2,3,3,2,3,1,2,2,3,2,1,2,3,2,2,3,2,2,1,2,1,3,2,1,1,2,3,1,2,3,2,1,1,1,2,2,2,1,2,3,3,3,3,2,2,3,3,3,1,3,3,2,3,3,2,3,3,3,3,1,2,1,1,2,2,1,1,1,2,3,3,1,3,1,2,3,1,2,3,2,1,3,3,3,2,1,1,1,3,2,2,1,2,3,2,2,2,3,1,1,2,1,2,3,1,2,1,3,2,2,2,2,3,1,1,1,3,1,3,2,1,1,1,1,3,1,2,1,2,3,1}
Returns: 101710332
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{2,2,1,1,3,1,4,3,1,4,2,3,3,2,2,1,3,1,2,4,4,2,1,2,2,1,2,3,2,3,1,2,4,3,2,3,1,4,2,2,4,1,4,3,2,4,4,2,3,3,1,3,4,4,2,1,2,1,4,3,4,3,2,3,3,3,2,2,2,2,2,4,4,3,3,1,1,2,2,3,3,2,1,3,2,1,4,1,2,2,1,2,4,2,2,2,3,1,3,3,3,1,1,3,2,1,2,3,2,2,2,1,4,4,3,3,2,3,1,4,2,4,2,4,1,2,4,2,4,1,3,1,4,2,4,1,3,1,2,1,4,3,4,4,4,3,3,2,1,2,4,1,3,4,1,2,2,1,3,3,1,2,4,3,2,4,3,4,3,4,1,2,2,3,2,3,1,3,3,4,3,2,2,4,3,4,4,3,2,2,1,1,4,1,4,1,3,1,3,3,1,2,4,3,4,2,4,2,1,1,2,3,4,4,1,3,3,3,1,1,3,2,3,4,1,1,2,3,1,1,3,3,1,1,3,1,3,2,2,4,1,1,1,1,2,4,1,3,1,1,1,2,1,1,1,4,3,4,3,2,2,4,2,2,3,3,2,1,3,4,1,3,4,2,4,2,4,4,3,4,1,2,1,3,1,3,3,2,4,4,2,1,3,2,2,2,4,1,2,3,2,3,4,4,4,2,1,3,1,3,3,1,3,2,3,2,3,3,3,1,1,1,2,4,4,2,3,3,2,3,1,2,2,4,1,2,4,4,3,2,1,1,1,4,4,3,4,3,1,3,2,2,1,1,1,3,3,3,1,3,2,4,3,3,2,3,2,1,1,1,2,1,3,3,1,2,3,2,2,1,3,2,3,4,1,1,1,1,2,2,1,3,4,1,2,4,1,2,1,2,3,2,4,1,4,3,1,1,3,4,2,3,1,3,3,1,2,3,4,4,4,4,1,1,1,2,2,4,1,1,1,4,1,2,3,3,3,2,1,2,4,2,3,4,2,1,4,4,3,2,1,1,3,1,4,2,3,1,3,3,2,4,2,3,1,3,1,2,2,3,4,1,3,2,4,3,2,2,2,3,2,2,3,2,1,3,1,2,2,3,3,3,4,3,1,4,2,2,1,1,4,4,2,4,4,3,4,1,1,1,2,2,4,4,2,3,4,3,4,3,3,3,4,3,4,3,2,3,3,1,2,2,4,2,1,1,4,3,1,1,4,1,4,3,3,2,3,4,3,3,3,3,2,2,4,2,2,3,1,1,4,3,4,3,2,1,1,3,4,1,1,3,1,1,4,2,3,4,4,2,1,3,1,1,3,4,1,4,4,1,3,1,3,4,2,4,4,2,1,2,3,2,2,4,4,3,4,4,3,3,1,1,2,4,1,1,3,2,1,3,4,4,1,1,4,3,1,1,1,2,1,2,4,3,1,2,2,4,1,4,4,1,2,1,2,3,1,1,2,2,4,2,4,2,1,1,1,4,3,4,1,1,2,2,1,1,3,2,2,1,4,4,4,3,2,2,3,1,3,2,2,4,1,2,4,4,1,4,4,4,4,2,2,1,4,2,3,2,4,4,3,2,4,3,3,3,3,4,2,1,1,2,4,4,4,3,3,1,1,1,4,3,2,2,1,2,3,1,4,4,3,3,2,3,3,4,1,4,4,2,2,4,3,3,2,4,1,2,2,4,1,2,4,2,2,2,1,2,1,4,2,4,3,3,1,2,1,4,1,1,2,4,1,1,1,2,2,3,4,1,2,4,4,2,4,2,3,1,1,2,1,3,4,2,2,1,4,3,2,4,2,4,4,4,3,1,3,2,2,4,2,3,3,1,3,1,3,2,1,3,1,3,1,1,3,3,3,2,1,4,3,1,4,2,3,2,2,2,4,1,4,1,1,4,4,2,4,2,1,4,3,4,1,3,1,2,4,2,2,1,1,4,1,4,4,3,3,4,3,2,2,2,4,2,3,4,1,3,1,4,1,1,3,2,3,4,3,3,4,2,2,4,2,4,2,4,2,1,4,4,2,4,3,1,4,4,4,3,4,2,2,2,2,4,1,3,2,3,4,1,3,2,2,4,1,1,2,1,2,2,3,4,4,3,3,1,2,1,1,4,4,3,3,2,2,4,1,3,4,3,2,4,4,3,2,4,1,2,1,3,2,1,2,4,4,4,3,3,3,2,1,1,2,3,2,2,4,4,3,4,2,2,4,3,2,4,2,4,2,2,1,1,4,1,3,2,4,2,2,4,1,4,3,4,2,4,2,1,4,2,2,4,4,4,3,1,3,1,1,1,2,1,1,1,1,3,4,1,3,3,4,4,1,4,3,2,4,4,2,4,1,4,2,2,3,2,3,3,2,2,3,3,4,2,4,3,4,4,1,1,2,2,1,1,2,1,4,3,3,3,1,1,2,4,1,2,1,3,4,1,2,3,3,3,2,4,2,2,4,3,1,3,3,4,2,4,2,1,2,1,1,4,3,2,2,1,3,3,2,3,4,2,1,1,2,4,1,3,2,2,1,1,3,3,4,1,1,3,3,3,3,1,3,4,4,2,4,3,3,2,3,2,1,2,1,2,4,2,1,3,3,4,1,4,4,4,4,4,4,3,1,2,1,2,3,1,2,4,3,3,4,3,2,1,1,3,3,3,4,4,4,2,2,4,3,2,4,3,3,4,4,1,2,2,3,2,2,2,4,3,3,1,3,2,3,3,1,4,2,3,4,3,3,2,4,1,4,1,2,3,1,2,1,3,1,3,2,1,1,2,2,4,1,2,4,1,1,3,3,3,4,3,1,1,2,2,3,3,4,2,4,1,2,2,2,3,2,3,1,3,1,2,4,4,4,1,1,4,4,1,1,2,4,3,2,2,3,4,2,4,2,1,3,2,4,2,3,4,2,1,1,3,1,4,3,2,2,1,1,4,2,3,2,3,4,2,3,1,3,4,3,1,1,2,1,4,1,3,2,2,1,4,4,4,2,1,3,2,3,3,2,1,4,3,4,1,4,1,3,3,2,2,4,2,3,2,2,2,1,3,2,1,2,2,1,4,1,1,4,3,3,4,4,3,2,4,3,1,3,3,4,1,4,2,4,3,4,2,1,4,4,4,1,4,2,1,2,4,4,1,2,2,1,1,4,4,2,3,3,4,4,2,2,3,3,2,3,1,4,2,4,1,3,4,3,1,4,4,2,3,3,1,3,3,2,1,4,2,1,4,3,3,1,3,3,1,1,4,1,3,2,1,1,1,4,1,2,4,4,2,2,3,1,1,3,1,1,2,1,3,2,4,1,4,1,2,3,2,4,2,1,3,1,2,2,1,2,3,2,4,1,1,3,4,1,1,1,1,4,3,1,3,4,2,3,3,2,4,3,3,3,4,3,3,2,2,3,4,4,4,1,1,2,1,4,2,2,1,1,4,1,2,2,4,2,4,3,1,1,4,4,3,3,1,3,4,2,4,4,3,4,3,1,4,4,4,1,1,2,3,3,4,1,4,1,3,4,3,2,1,4,3,1,2,4,4,4,1,1,3,4,4,1,4,3,3,2,3,2,1,1,4,1,1,2,2,3,1,1,1,4,2,2,3,2,3,2,2,2,2,1,2,1,3,2,2,3,3,2,3,3,1,3,2,3,3,2,3,3,2,4,1,1,1,3,3,4,4,4,3,1,4,4,3,4,3,3,3,2,2,2,4,1,1,1,1,1,4,3,1,2,4,4,1,1,2,4,4,1,3,4,3,1,4,3,2,1,2,2,2,3,4,4,3,2,1,3,1,1,3,1,4,1,1,3,1,1,2,3,2,2,1,2,2,1,4,4,4,2,4,1,4,3,2,4,2,1,2,2,1,4,1,1,4,4,3,4,2,1,3,2,2,1,1,4,3,4,4,1,2,3,4,4,1,1,3,4,3,2,1,2,4,1,1,3,4,2,2,2,3,2,3,3,4,4,3,2,2,2,4,3,3,3,1,2,3,1,1,3,2,2,1,3,3,3,4,2,3,3,3,1,1,3,4,4,3,1,3,4,2,1,1,1,3,1,3,4,1,2,1,2,2,1,3,1,4,2,2,4,1,2,2,4,2,1,1,3,2,4,2,2,2,3,3,2,2,1,1,2,3,4,4,2,4,1,1,2,1,3,2,3,1,4,4,4,4,2,1,3,2,4,4,2,3,2,2,1,1,1,4,1,3,4,1,1,4,1,1,1,1,3,4,3,2,1,2,4,1,4,1,2,2,3,4,2,3,1,1,1,1,1,2,2,4,3,3,4,4,2,3,2,4,4,2,1,4,3,1,3,1,4,4,3,1,2,1,1,2,3,1,3,3,4,3,1,3,2,2,1,4,3,1,2,1,3,4,4,1,1,3,2,3,1,3,2,2,1,4,2,1,1,1,2,2,1,2,2,2,3,1,1,1,4,4,3,3,1,1,2,1,1,1,1,3,4,3,3,1,4,4,2,1,1,3,3,1,2,1,4,1,3,1,4,4,1,3,4}
Returns: 436587567
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{1,1,4,3,4,2,2,3,1,4,4,1,2,1,2,4,3,2,3,2,2,1,2,2,1,3,1,3,4,3,4,3,4,2,1,4,2,2,3,1,4,2,4,2,1,1,2,4,3,2,4,2,1,3,1,4,2,1,1,1,3,2,2,3,1,3,2,1,1,1,4,2,3,3,4,4,1,2,1,2,1,2,3,3,4,1,3,3,4,3,4,3,1,2,2,2,1,4,3,4,2,2,1,2,2,3,4,1,2,1,4,2,4,4,1,3,4,3,1,3,3,2,3,2,3,4,1,3,3,3,3,3,1,1,1,1,3,2,1,2,2,4,3,3,1,3,2,3,1,1,2,2,4,2,3,4,2,1,4,4,1,2,1,2,1,3,3,2,4,2,4,2,1,1,4,2,4,3,4,2,1,1,3,2,1,4,2,1,3,1,3,1,4,2,3,3,2,4,2,4,2,3,2,2,2,4,2,3,1,3,1,3,3,3,1,3,3,2,4,4,2,3,3,4,3,3,3,4,3,4,4,1,1,4,4,3,2,2,3,3,4,4,3,2,2,4,1,4,4,2,4,4,2,1,3,4,1,3,2,3,2,2,4,4,2,4,1,2,2,1,3,2,2,2,3,1,2,4,1,3,3,2,2,1,2,4,1,2,4,1,2,2,4,1,1,4,2,2,3,2,3,3,1,4,3,1,1,4,2,1,1,3,1,3,1,4,3,1,4,2,4,1,4,1,4,4,4,2,1,4,3,4,1,3,3,1,2,1,2,2,4,3,1,3,3,2,4,4,4,3,1,3,2,1,4,2,4,2,2,1,3,1,4,3,3,1,2,1,2,1,2,4,1,1,2,3,3,1,2,2,4,4,4,3,4,1,4,2,1,3,1,4,2,2,2,1,4,3,4,3,4,1,2,4,4,4,3,2,4,2,1,3,1,1,3,3,2,1,4,3,4,2,4,2,2,3,1,4,4,4,3,1,1,3,3,4,4,2,2,4,4,4,1,1,3,4,4,3,3,3,4,3,1,2,4,2,2,3,1,1,2,4,4,1,3,3,3,1,2,2,2,3,1,2,1,1,1,4,1,1,4,2,1,3,4,4,3,3,1,1,2,2,1,2,3,4,4,3,3,2,4,2,3,1,2,3,4,1,4,3,2,4,2,4,3,1,3,3,2,4,4,3,2,3,3,4,2,1,3,4,2,4,2,4,2,2,2,3,1,2,3,2,4,1,1,3,3,2,4,1,1,4,3,1,3,4,2,3,2,4,4,1,2,3,3,2,1,2,4,1,4,3,3,1,3,1,3,3,3,2,3,4,1,4,3,1,2,3,1,1,4,1,2,2,1,3,1,1,2,3,3,3,3,1,2,4,1,4,2,2,3,2,3,3,4,4,1,4,4,4,3,2,1,2,3,2,3,4,2,2,3,3,4,3,2,2,3,1,1,3,4,2,2,3,1,3,2,1,1,3,4,3,2,4,1,1,1,1,3,4,1,3,2,2,2,4,4,4,2,2,3,1,2,1,1,2,3,4,1,1,3,2,4,2,3,2,1,4,4,1,1,1,4,3,4,2,3,2,3,3,1,3,1,4,1,1,2,4,3,1,1,1,3,4,3,3,4,2,4,2,1,4,2,2,2,1,2,2,4,3,1,2,1,4,1,3,3,2,3,3,2,4,3,1,1,3,1,2,4,3,4,3,4,2,4,2,3,1,3,4,4,4,2,2,1,2,4,3,2,2,2,2,4,1,4,3,4,2,3,1,3,4,1,2,3,4,2,3,2,1,2,4,3,1,3,3,3,1,2,1,2,2,2,3,3,2,4,3,4,2,2,1,2,2,3,4,4,4,1,2,4,1,1,1,3,2,4,1,2,1,3,2,2,1,4,3,3,3,3,2,4,4,3,4,4,4,1,1,3,1,2,4,3,2,1,1,2,2,4,3,2,1,1,3,1,4,1,3,3,4,4,4,3,3,1,3,1,1,3,3,4,1,1,4,3,3,4,3,3,1,3,3,3,4,4,4,2,1,4,1,1,4,1,2,2,3,1,3,3,2,3,4,1,1,1,1,1,4,1,1,4,4,4,1,4,2,2,2,1,3,4,2,1,4,4,3,2,3,1,4,4,4,1,4,2,2,3,4,1,1,3,3,1,1,1,3,2,1,1,3,2,1,3,4,1,1,1,2,3,4,1,3,4,2,1,2,3,2,3,3,4,4,2,2,4,1,1,2,1,1,3,1,3,2,2,3,2,1,4,1,4,1,3,4,2,2,4,1,1,2,2,4,3,4,3,1,4,1,3,3,1,4,3,4,2,3,2,4,3,1,1,2,4,4,3,4,2,2,3,3,3,1,2,1,3,1,3,1,1,4,3,3,4,1,1,3,3,3,2,2,3,3,3,4,4,2,2,1,4,2,3,2,1,3,3,2,1,3,4,2,4,1,3,4,4,4,1,1,4,3,3,3,1,3,4,2,2,4,1,4,4,4,4,1,2,3,3,4,3,1,3,1,1,2,2,2,4,1,1,3,1,3,2,4,2,1,4,4,4,4,2,1,3,2,2,2,3,2,4,2,2,1,2,2,3,3,4,2,2,2,1,3,4,2,4,1,4,2,1,4,4,4,3,1,1,3,2,2,3,4,4,2,3,2,1,3,1,1,4,2,2,3,4,4,3,4,1,2,3,3,2,4,3,1,4,2,2,4,4,2,4,1,1,1,4,4,2,4,2,4,3,3,1,3,1,2,1,2,3,1,1,3,1,4,3,1,3,1,2,4,1,3,2,2,4,4,4,3,4,3,3,2,2,3,1,3,3,3,4,1,1,2,2,4,3,4,2,2,4,1,4,2,1,1,2,3,1,3,1,4,2,4,3,1,2,2,3,4,2,1,3,1,4,2,2,2,4,3,4,3,3,4,1,2,4,4,4,3,3,2,1,2,1,4,1,1,1,2,2,3,1,3,2,3,2,3,2,3,2,3,2,4,2,1,4,3,4,4,3,3,1,1,1,2,4,2,2,1,4,2,4,1,1,4,4,3,1,2,2,1,3,3,2,2,2,4,1,4,1,3,2,2,4,1,2,1,3,4,4,2,2,3,4,4,1,3,3,3,2,4,3,1,3,2,1,4,1,3,3,3,3,4,4,1,4,2,3,2,4,1,4,2,4,1,1,2,1,3,2,1,3,4,4,4,4,4,3,3,3,3,2,1,4,3,4,3,1,2,3,2,2,1,2,1,1,4,4,2,4,3,2,1,4,3,2,1,3,2,4,1,2,2,4,2,2,2,4,2,2,4,3,4,2,1,3,2,2,2,2,4,1,3,4,2,4,2,3,4,4,1,2,4,4,3,1,2,1,2,3,1,1,4,3,1,3,4,3,1,3,2,4,4,4,2,3,4,2,4,3,3,1,1,2,2,1,3,3,4,2,1,2,3,3,3,1,4,3,2,3,4,2,4,1,3,2,1,1,4,4,1,2,4,1,2,4,1,4,1,2,4,3,2,2,4,2,3,3,2,2,2,3,1,1,4,3,2,3,1,1,1,1,1,2,4,3,2,2,1,1,3,2,2,1,2,3,1,1,2,2,2,2,2,2,4,4,2,3,3,2,3,2,1,4,4,3,1,2,4,3,3,3,2,4,4,4,4,2,1,4,3,4,1,3,1,4,2,2,3,3,4,1,4,2,3,1,3,2,1,4,3,3,3,3,4,3,4,2,4,3,2,2,3,4,2,1,4,3,2,1,3,2,2,1,1,3,2,3,1,2,2,3,4,3,2,4,2,4,1,4,4,4,2,4,1,2,1,4,2,3,2,1,1,3,2,1,2,4,4,1,1,3,1,2,4,2,4,1,3,1,4,4,3,1,4,2,2,3,3,3,4,1,4,3,4,3,3,3,2,3,3,1,1,1,1,3,2,4,4,3,4,1,3,3,3,4,4,4,3,2,2,1,2,1,2,1,2,2,4,2,2,4,2,1,2,1,4,4,2,1,2,3,1,3,1,1,2,2,2,4,3,1,2,2,2,1,4,1,1,4,3,2,3,1,2,1,4,2,2,3,4,4,4,3,1,1,4,3,3,3,3,3,3,1,2,2,4,1,1,3,4,1,1,3,2,2,1,4,3,1,1,3,4,1,4,3,2,1,2,4,4,4,3,3,2,3,3,1,3,2,2,3,2,2,2,1,2,3,3,1,4,2,4,2,1,2,2,4,1,3,4,1,1,2,3,4,1,4,2,2,1,1,2,3,3,4,4,2,4,3,2,1,4,2,1,1,4,2,2,4,4,2,1,4,1,1,2,1,1,2,2,1,3,2,4,2,2,1,3,2,3,4,4,1,2,1,3,4,1,4,2,3,1,4,4,2,3,4,1,3,1,2,1,1,1,2,4,4,2,4,4,1,2,4,4,4,4,1,4,2,2,4,1,4,3,1,1,2,1,3,1,1,3,3,3,2,3,1,3,4,4,3,1,2,3,2,4,3,4,4,1,4,3,1,3,4,1}
Returns: 855745131
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{2,3,1,3,1,1,2,1,4,1,1,3,2,3,3,3,2,3,3,4,3,4,2,1,3,4,1,4,2,1,4,4,1,4,3,1,4,1,3,3,2,2,3,2,3,4,3,1,2,2,1,4,1,3,1,4,1,4,1,4,2,1,4,4,4,1,3,4,1,4,2,2,2,4,3,3,1,2,1,3,4,4,2,1,3,4,1,2,4,1,2,1,4,3,4,2,4,3,4,2,3,1,3,4,4,4,4,2,2,3,1,4,4,3,4,2,4,3,2,3,3,2,2,3,1,3,1,4,3,1,1,3,3,3,4,4,1,1,3,3,1,2,3,4,3,3,1,4,4,4,4,3,1,3,1,4,2,3,2,3,2,4,2,1,4,1,1,4,4,1,1,1,2,4,2,2,4,4,3,1,3,3,1,4,4,1,4,4,4,3,2,4,4,2,3,3,4,4,1,4,2,2,4,4,2,3,2,2,4,2,2,2,4,1,3,3,4,2,4,4,2,4,1,4,2,3,1,2,3,2,1,3,4,3,2,1,2,1,3,4,3,3,3,2,3,3,1,1,2,4,1,3,4,4,2,1,2,4,2,3,2,2,2,2,2,3,2,2,1,3,3,3,4,4,1,3,2,2,3,4,2,4,4,1,1,4,2,4,4,2,2,3,1,1,1,2,3,1,2,2,2,1,1,1,1,2,3,4,4,1,3,4,2,4,3,3,3,2,2,2,1,2,2,1,3,4,2,3,3,4,2,3,1,2,2,2,3,3,2,4,1,2,2,1,1,3,1,2,3,2,4,4,4,2,1,4,2,2,1,4,1,1,1,2,2,4,4,4,1,4,1,2,4,1,2,2,1,3,3,1,2,1,2,3,4,3,1,3,3,1,4,4,4,3,3,2,1,3,1,3,1,4,2,3,3,4,1,4,2,4,1,3,1,3,2,2,4,4,2,3,1,3,3,1,1,2,2,3,4,3,3,4,2,2,3,2,4,4,2,1,3,4,4,2,2,4,1,3,3,4,2,1,3,1,1,4,3,3,1,4,3,3,1,2,2,4,1,3,1,4,3,3,4,4,2,1,3,3,4,1,1,4,2,4,4,2,1,4,1,2,4,4,3,1,1,1,1,4,3,4,1,4,1,4,3,4,4,1,4,4,1,2,4,2,3,4,3,4,2,1,1,1,3,4,1,3,2,3,3,4,3,2,1,1,2,2,2,3,4,3,4,4,1,1,4,4,3,3,1,3,1,2,2,2,3,1,3,3,2,4,1,4,3,2,2,4,4,1,2,4,4,3,2,2,4,4,1,1,2,1,3,2,4,1,4,4,4,2,3,4,4,2,1,1,1,1,4,1,4,4,3,3,4,2,4,4,1,3,3,4,4,3,2,4,3,2,1,4,4,3,2,3,3,1,4,3,1,2,4,4,2,1,1,4,2,4,1,3,3,4,4,2,2,4,2,2,3,2,4,3,2,4,3,4,1,3,3,3,2,4,3,2,3,4,1,1,1,3,3,2,3,4,2,3,4,2,1,2,3,4,3,1,4,1,3,1,1,1,3,2,3,1,4,2,3,4,3,2,3,3,1,1,4,3,4,1,2,1,4,4,3,2,2,4,3,4,1,2,3,4,1,3,3,4,4,1,2,2,1,2,2,2,2,3,4,1,4,3,2,4,2,2,1,1,2,1,3,4,2,4,4,2,1,1,2,3,3,2,1,2,1,1,1,2,1,4,2,3,4,4,4,4,4,2,3,1,3,2,4,3,3,1,3,3,2,3,3,4,2,4,4,3,4,1,4,3,4,3,2,4,1,1,2,3,4,2,3,1,1,4,2,2,4,1,1,4,1,1,3,3,1,1,1,3,1,4,3,2,1,2,4,2,2,1,2,4,1,4,4,4,3,4,1,2,4,2,2,1,4,4,1,4,2,3,2,3,2,3,3,4,1,1,3,4,4,4,4,1,4,4,3,1,1,2,2,3,3,1,3,1,4,2,4,4,1,1,1,3,4,3,2,4,3,2,4,3,2,1,3,2,4,4,3,4,3,3,1,2,1,4,1,3,1,3,3,2,1,3,1,2,3,2,2,3,2,2,3,3,1,1,4,1,3,3,1,4,3,1,2,2,3,4,3,1,1,2,3,4,1,3,3,3,1,1,3,4,1,1,4,4,4,2,3,2,4,4,4,1,2,4,1,2,2,2,3,3,1,4,1,1,1,4,2,2,1,2,3,1,3,4,4,3,1,4,2,2,1,3,2,3,1,3,2,1,2,2,3,1,2,3,1,4,4,3,3,1,1,2,1,4,1,4,4,3,3,1,4,3,3,4,3,3,2,3,3,4,4,3,2,3,4,4,3,1,2,4,3,1,4,2,3,3,4,4,3,3,1,3,4,1,1,1,3,3,2,4,3,2,1,3,1,1,3,3,3,3,3,4,1,3,3,1,4,3,1,2,3,3,1,1,4,4,3,3,4,1,4,1,4,1,1,1,2,2,3,3,1,1,2,2,4,2,2,3,3,1,4,3,1,2,2,2,3,3,1,2,1,1,1,3,1,2,3,1,1,3,3,1,2,1,2,2,1,4,3,4,3,2,2,3,4,2,1,4,1,4,1,3,1,3,3,3,4,4,4,1,2,2,1,2,1,2,2,3,4,3,4,4,2,4,2,1,1,3,2,1,1,3,1,1,1,4,4,1,3,2,2,3,4,4,2,2,2,3,3,1,2,3,3,3,3,1,4,4,1,1,1,4,4,3,3,2,3,4,4,1,3,4,3,1,1,4,2,2,4,3,3,3,3,3,4,2,3,2,4,4,4,4,4,3,2,3,4,3,2,2,4,2,4,1,3,4,3,2,4,1,3,4,3,2,4,2,3,2,4,1,3,3,4,2,3,4,2,4,1,4,4,1,1,2,1,1,4,4,1,1,4,1,2,3,4,2,1,3,2,4,2,1,4,2,3,1,1,4,2,4,1,4,2,3,4,4,4,4,2,4,2,3,3,4,2,1,4,4,2,1,3,1,4,3,1,3,2,3,2,4,1,4,1,4,2,2,3,4,1,2,4,1,4,1,4,4,1,4,4,4,1,4,4,3,1,2,1,2,2,4,4,4,1,2,4,4,4,2,3,1,1,2,4,4,1,2,2,4,2,4,1,1,4,2,4,3,4,1,1,2,3,1,4,2,2,2,4,2,4,3,4,2,1,2,2,4,1,2,1,3,4,3,2,1,2,4,3,2,1,1,3,2,4,4,1,4,4,4,1,2,1,2,4,1,4,1,2,3,2,2,4,3,1,1,2,1,3,4,3,3,3,2,4,3,4,2,2,4,4,2,4,3,1,1,1,2,4,2,3,3,1,4,3,2,2,2,4,1,4,2,2,1,1,1,1,2,1,3,2,2,4,3,3,2,2,3,1,2,1,2,1,1,1,4,3,4,4,1,2,1,2,4,4,1,3,1,2,4,2,4,3,4,1,3,3,3,1,2,1,4,3,3,3,1,1,4,4,4,3,4,3,4,3,2,1,2,1,4,1,2,1,1,4,4,4,1,4,3,1,4,3,4,3,1,4,1,4,2,3,3,2,3,2,2,2,3,4,3,1,1,4,2,2,1,3,4,2,1,3,3,2,4,4,3,4,3,3,1,2,4,4,3,4,4,1,3,3,3,2,2,2,3,2,4,3,3,4,2,2,3,1,4,1,3,2,4,4,1,1,1,4,2,2,4,3,1,1,4,1,3,3,4,2,1,4,3,4,3,3,2,4,1,3,1,1,3,4,1,4,1,3,1,3,1,4,2,4,2,3,3,2,1,3,4,4,1,3,2,2,4,1,2,3,4,2,1,1,2,4,2,1,1,2,4,3,2,4,1,2,3,1,4,4,4,4,1,2,3,2,1,3,2,4,1,3,1,1,3,3,1,4,4,1,3,2,3,4,2,2,4,4,3,1,4,4,3,3,2,1,4,2,4,1,3,4,3,1,2,2,3,4,2,2,4,4,2,3,3,1,1,2,1,4,1,2,3,2,4,2,2,2,1,4,4,4,2,2,1,1,3,4,2,2,3,2,4,4,2,3,4,3,4,2,1,3,4,1,1,4,1,1,3,3,4,2,3,2,3,2,3,3,2,2,4,4,4,4,1,4,3,3,1,2,2,3,1,3,3,1,4,4,3,3,3,1,1,4,1,1,3,3,2,2,4,3,3,4,2,2,4,4,3,4,3,3,2,3,4,2,3,2,4,1,4,4,1,4,3,2,2,2,4,2,2,2,4,4,2,4,4,4,2,3,3,1,1,2,1,1,3,4,2,2,2,1,4,1,4,1,2,1,3,2,2,3,2,1,3,4,2,3,3,2,3,3,2,1,3,1,3,1,2,1,2,1,2,1,4,1,1,3,3,4,4,2,3,3,3,2,3,3,1,3,1,1,4,4,4,3,4,3,4,2,2,1,1,4,2,2,1,3,3,1,3,1,4,2,4,1,4,2,2,1,2,1,3,4}
Returns: 839675048
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{1,4,4,4,2,4,4,2,1,1,3,3,4,1,1,1,2,2,1,2,3,4,2,1,4,2,4,2,1,2,4,4,3,1,4,2,2,2,3,4,3,3,4,3,2,1,1,1,4,3,4,3,3,1,3,4,4,3,4,2,2,3,3,2,3,1,2,1,1,4,1,2,1,2,2,4,1,4,4,1,2,2,4,2,3,2,1,4,1,4,2,4,1,3,4,2,4,4,2,4,1,1,3,4,4,4,1,3,1,4,4,4,4,4,2,2,4,1,1,2,1,1,1,1,4,3,1,2,2,2,4,2,2,2,2,2,4,2,4,2,3,3,2,4,4,3,1,3,1,4,2,3,4,4,1,4,2,2,3,4,4,2,1,4,1,3,1,1,1,1,1,3,2,2,1,1,2,1,3,1,2,3,3,1,4,3,1,1,1,4,2,4,3,3,1,4,1,3,3,1,3,4,1,1,4,1,1,2,2,2,3,4,1,2,2,4,2,1,2,2,1,1,3,2,3,2,1,3,3,2,4,3,4,2,3,4,2,3,4,3,2,3,1,2,1,2,1,3,3,1,2,1,2,4,1,2,4,4,1,1,1,3,2,3,4,1,1,4,1,3,1,3,2,3,1,4,4,1,2,1,1,2,2,3,3,1,1,3,3,2,1,2,4,1,1,2,3,1,4,4,1,4,2,3,3,1,2,3,4,3,4,4,2,3,3,1,1,2,2,3,2,3,2,3,1,1,1,1,3,3,2,4,4,1,2,2,4,1,1,4,3,1,1,1,1,2,1,2,2,2,4,2,1,2,3,4,4,1,4,2,1,4,4,4,4,4,2,3,3,2,2,2,2,2,2,4,1,1,3,2,1,2,2,4,2,4,1,4,1,4,4,3,1,2,1,4,1,1,1,3,2,3,3,3,4,2,1,4,3,4,4,2,3,1,3,1,4,1,4,1,3,4,1,1,4,2,4,3,1,4,2,2,3,1,1,1,4,3,3,3,3,4,1,3,3,1,3,1,3,4,1,1,2,2,4,3,2,1,3,3,3,1,1,2,1,3,2,3,2,4,3,3,3,2,2,3,2,1,4,2,4,3,3,1,3,3,3,4,3,4,3,2,2,2,2,2,1,4,3,2,4,3,2,3,3,2,3,4,1,1,3,2,2,2,4,1,4,2,3,4,4,2,1,1,4,2,3,2,1,4,1,1,2,4,1,4,1,3,1,3,3,2,1,4,4,3,2,3,1,1,1,4,3,3,3,3,4,4,3,3,3,4,4,2,3,1,2,1,4,3,4,4,3,2,3,3,3,4,3,4,4,1,1,1,2,3,1,4,2,3,3,4,4,1,3,4,4,1,1,4,1,3,4,3,2,3,3,1,3,4,3,4,4,3,2,4,3,1,4,2,3,4,3,1,1,3,1,2,3,4,2,1,2,2,4,4,1,4,2,4,1,3,3,2,3,2,3,1,2,3,3,1,3,2,1,2,4,2,4,3,1,3,2,1,4,2,2,3,4,1,4,1,2,2,3,3,4,3,3,2,2,3,4,4,2,4,4,2,3,3,3,2,4,2,4,1,1,4,4,2,4,3,2,2,1,2,4,3,1,1,3,4,1,2,2,4,1,3,4,1,1,2,4,2,2,3,4,1,1,4,2,2,1,3,4,3,3,1,4,4,1,1,3,4,2,4,3,4,1,2,2,3,3,3,3,1,1,1,3,3,3,3,2,1,4,4,4,3,3,4,3,1,1,1,3,2,2,2,1,1,1,3,4,4,1,4,2,2,4,2,2,1,3,2,3,1,2,3,3,3,1,4,3,2,1,1,2,4,4,1,3,1,4,1,3,2,1,4,4,3,1,4,4,1,3,3,1,1,3,2,4,3,2,3,2,4,1,1,1,4,1,1,3,3,1,2,3,3,1,1,2,2,3,4,3,2,1,4,4,2,1,4,2,2,1,1,1,4,4,3,3,4,1,2,4,1,4,4,1,4,1,4,1,4,4,1,2,4,1,3,3,1,3,2,2,3,1,4,4,4,2,3,4,4,3,2,3,4,3,3,3,3,2,4,2,2,3,3,4,3,3,4,4,3,4,1,3,3,2,1,4,1,1,1,3,4,1,4,1,4,3,2,3,2,4,3,1,3,1,1,2,4,4,2,3,3,2,3,3,4,3,3,4,4,2,2,4,4,1,4,3,4,4,1,2,4,4,1,2,2,3,3,3,1,1,3,2,1,4,1,4,3,3,3,2,4,1,3,1,3,3,1,4,4,1,2,1,2,1,1,1,1,4,3,2,2,4,1,3,3,3,1,1,4,2,2,2,3,4,4,2,4,4,4,3,4,3,1,4,3,4,3,2,2,2,4,2,4,1,2,1,1,1,2,3,3,1,4,1,1,4,4,2,4,1,2,1,3,3,3,2,1,4,4,2,2,1,1,1,4,4,3,4,3,2,4,4,1,2,2,4,2,4,4,1,4,1,4,2,2,3,2,4,1,3,3,1,4,1,4,2,4,1,1,2,2,3,4,4,1,4,4,2,4,4,3,1,1,2,3,3,2,4,1,1,4,4,1,1,2,4,4,3,4,4,2,2,2,1,2,4,2,3,2,2,2,1,4,1,2,4,1,2,3,1,4,3,2,3,2,1,1,3,4,1,1,3,3,2,4,1,4,2,3,4,1,2,2,4,2,4,2,2,1,1,4,4,1,1,4,1,1,2,1,3,4,4,1,2,4,3,2,2,4,4,4,1,3,3,4,2,4,2,3,3,3,3,2,4,2,2,2,2,2,4,2,2,4,3,4,4,3,2,3,1,2,2,2,1,2,2,3,4,3,3,1,1,4,1,4,4,3,2,4,4,2,3,4,2,3,3,4,2,1,4,3,2,4,3,3,3,1,3,4,3,1,4,4,3,3,3,1,3,4,1,3,3,4,2,1,4,4,4,1,4,3,3,1,4,1,2,1,3,1,4,4,4,2,3,2,4,2,2,1,1,1,3,4,4,4,4,1,3,3,1,3,1,2,2,3,3,2,2,2,2,3,1,2,3,2,2,3,4,3,4,3,3,4,4,3,4,2,4,4,2,1,4,1,4,2,4,2,4,1,2,3,2,4,2,1,1,1,1,4,3,3,1,2,3,1,4,3,3,1,4,2,2,4,4,4,1,3,1,2,3,1,4,1,4,4,2,2,3,2,2,4,2,3,1,3,1,4,1,2,2,2,3,1,1,3,1,2,4,4,1,4,3,2,1,3,4,2,2,2,4,4,1,1,4,1,1,4,2,4,3,3,4,2,3,2,1,2,3,4,1,4,3,1,4,1,1,1,2,4,1,1,4,3,3,2,3,4,1,1,4,1,3,3,2,2,1,4,4,1,1,1,4,2,4,1,1,1,2,4,1,3,3,2,1,4,4,3,4,3,3,3,2,4,1,1,1,3,3,2,3,1,2,4,4,2,2,2,3,1,4,3,4,2,3,1,3,4,2,1,1,3,3,1,2,3,4,4,4,3,2,2,1,3,2,4,2,3,3,4,1,1,1,2,2,2,3,1,1,1,3,3,2,4,1,2,4,1,2,1,3,4,2,3,2,1,3,2,1,4,2,4,2,3,1,1,1,4,2,3,2,4,1,4,2,4,3,3,1,1,2,1,3,3,1,1,1,3,3,2,3,4,4,1,3,3,3,2,1,1,4,1,2,2,4,3,1,1,3,1,3,3,4,4,4,3,4,2,1,3,1,3,3,1,4,3,2,1,2,1,4,2,1,2,2,4,2,1,3,2,1,3,2,3,4,1,2,3,3,1,3,4,1,1,2,2,3,1,2,1,1,3,1,4,3,2,3,2,1,2,2,2,4,3,4,1,1,2,1,3,1,4,1,4,1,4,1,1,1,4,1,1,3,1,3,4,3,2,2,1,4,2,1,3,2,3,4,3,4,2,1,3,2,4,1,3,1,3,3,4,1,3,1,4,1,2,4,2,4,4,1,4,4,4,3,3,3,3,4,3,2,4,1,2,4,4,2,3,2,4,1,3,2,1,2,4,1,4,2,4,1,1,4,4,3,2,4,4,1,1,2,1,4,1,1,2,4,3,1,2,2,1,1,2,2,4,2,4,4,1,2,4,1,3,4,4,3,3,3,1,1,1,1,4,1,4,1,1,2,2,1,4,2,1,3,3,4,2,3,2,2,4,2,2,2,1,3,3,1,3,4,3,1,4,2,2,3,4,4,1,3,3,1,3,2,4,3,4,4,3,3,2,3,4,1,3,2,2,3,3,3,1,3,1,4,3,3,3,1,1,2,4,2,2,1,3,3,3,4,2,1,4,1,3,4,3,1,1,4,1,1,1,1,4,2,3,2,1,3,4,1,2,4,2,4,1,3,3,2,4,4,1,4,1,3,2,2,2,4,2,3,3,2,1,3,4,4,3,1,2,2,2,4,2,4,1,1,4,1,2,2,1,4,1,1,4,4,4,2,3,4,1,4,2,4,1,1,1,4,2,4,1,1,4,3}
Returns: 619677193
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Returns: 138586517
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Returns: 340332188
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Returns: 118040038
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21,4783,6461,9069,746,7570,2844,5630,4401,898,6928,2098,374,7044,9115,6545,7339,6205,7372,701,10000,8911,1826,5587,30,3132,6227,9642,5561,7157,9657,7485,9854,3577,2947,1290,7013,1986,5766,8000,8914,7578,8250,4699,7021,8028,2577,1776,2584,5204,4621,7816,6350,181,3601,2743,8457,2811,5645,7428,7594,2245,4315,5411,9870,2673,9400,9851,9102,5704,6625,8685,2073,7742,1625,4097,8372,6897,9763,8387,2695,34,4576,706,6444,5795,3303,6778,5450,311,6166,8877,5653,8140,6197,4677,9489,9824,2421,9978,4965,9474,9676,380,1607,9336,899,3772,232,3259,9311,9242,3216,933,5058,2512,8613,3396,3871,4432,5358,3014,2568,7383,6509,2049,6678,5613,8580,6348,551,669,8575,373,6268,2849,1627,1321,2755,6538,8424,1818,5185,9571,3069,2091,5335,4810,3427,1678,1118,3675,5574,516,2549,3923,2213,4559,286,9819,1742,4862,687,5754,8718,8233,4189,6085,7278,4032,8428,7820,3453,5499,684,6176,7350,6341,7065,768,7057,7442,8107,9438,9707,3296,3473,7789,1975,968,6546,6696,5839,965,1381,671,1130,8935,3474,9473,6609,623,7480,5997,5383,6533,8997,1403,6222,8914,9324,3385,7247,5058,2916,336,4753,774,7468,8931,2547,1232,4721,9656,8346,335,6767,1746,5094,5340,5660,8299,9019,4702,4854,2599,7833,7010,6509,4258,9883,1970,5032,6558,703,441,7078,1131,78,7792,2533,4210,9717,3184,5496,3893,4193,2016,6540,412,6520,2201,3683,3714,8963,6030,1534,7006,4061,3517,4407,7075,9873,7279,6265,8894,4038,4502,6748,7658,6675,7728,1252,7546,3359,8519,46,5761,6216,5246,4035,3127,3033,3829,7504,1115,337,3792,6358,9935,5222,3282,5951,5456,698,2930,5950,7395,5551,7384,1432,4464,8533,2085,1994,5283,6498,8864,213,5739,9462,1360,2266,7469,8385,2337,2345,5244,797,438,7016,5189,4337,1639,3515,5636,2379,4831,7799,664,1351,4850,6876,3304,3556,2927,7279,2008,4593,1964,5261,2032,3415,9817,3930,4944,104,8485,8894,2110,1524,3977,3796,8760,5925,3956,2404,8907,2386,3248,7243,3155,9062,7909,5009,3752,8322,3843,7278,2920,4316,5771,7930,972,8811,869,6919,3770,352,5233,169,8660,3160,3240,8073,2055,6262,2966,7122,1376,2472,4326,9066,6449,9778,3992,8750,5415,8140,2933,9126,3761,7254,2101,7182,426,2240,6396,8670,1952,3709,1885,9756,1518,7525,359,7889,4918,9638,7992,8470,9512,3209,5291,3969,6432,275,5455,3234,6096,2892,6068,1746,3332,7193,9052,7358,7543,6182,7483,7407,2661,7849,355,7752,3888,3019,8555,3,5090,672,4110,528,92,6488,9303,8644,6559,6685,6573,6926,6413,658,8617,9869,2259,8521,4669,3798,6533,5243,1392,9901,4254,5465,4658,148,6937,8173,250,1331,8987,9194,7905,2064,3991,9834,2119,7462,3073,1878,7604,3261,7361,1281,3618,7055,939,9812,4868,2232,9348,1101,1700,2619,2736,2411,8787,4531,7743,2631,1130,7246,5972,9728,9343,9891,7936,2702,5507,9967,9075,8995,9668,3938,587,6318,4505,6673,8769,3993,5257,1793,6589,1396,2410,5123,9950,644,1398,3625,8967,3839,4796,7616,3023,6043,7905,4910,2908,1899,745,8656,4240,1885,6765,6765,3037,3259,4645,4675,7621,6718,4491,2897,3485,6969,8669,8765,9101,5559,3857,5470,7300,4378,4872,8040,2732,8931,8325,9002,5070,3198,477,8726,9342,3249,9512,6592,6756,6734,5087,4445,1595,7521,8776,6227,6556,3616,964,9459,279,9388,5293,4621,4214,4980,5218,536,5960,9943,7185,9998,4744,6879,878,7128,7974,5536,6798,3681,7232,8282,6224,1611,9602,1904,5660,7643,6244,5165,4875,4000,8345,3066,1943,6090,8331,7953,1985,6512,4644,2245,3137,2729,8172,1348,6339,8940,3176,1656,4965,8508,9498,886,1516,6128,6285,2059,3843,2367,8769,9264,4660,6006,3081,5968,1350,2923,6733,3925,6308,4647,3167,1892,9001,7487,8048,609,3654,9971,610,3216,5910,301,9813,7426,6691,9655,2876,5335,9105,9013,9653,2288,66,3861,462,9763,6547,1529,4151,5046,3522,8100,1485,9976,1949,1578,8415,8356,5531,5791,8784,2835,8584,2989,2653,8579,6566,6863,2888,9127,5790,1774,5984,8957,5133,5119,5811,4316,4141,8051,850,6677,3471,1274,794,9845,9458,9319,2472,8124,4917,4289,9258,7389,4341,7179,1159,1881,1507,2116,649,2772,5436,1817,878,3086,9951,4259,7412,4404,888,4534,3907,9192,4418,5987,3243,1199,5900,1933,6665,1795,5166,3576,6580,8245,1569,2732,8673,1980,7189,6372,1506,8286,6658,5750,9525,4126,2677,3948,795,1537,9381,7786,592,7414,662,9094,4074,3116,5451,4866,9204,4845,713,2185,9824,6800,7763,4874,6538,409,8474,320,8615,442,4930,2116,969,8935,6577,626,3337,6005,7279,6850,1727,9253,5050,8170,63,8708,3526,2810,4582,2780,1372,4350,991,5373,4086,1878,5086,5447,2349,2493,6039,3736,8271,6253,1206,6638,1911,9372,632,6458,9361,6893,381,6685,5872,2315,9096,8135,4261,7584,5483,996,8617,2840,7697,1012,9826,2692,6826,937,3410,7718,1811,2397,7763,4392,4777,2622,4341,8794,494,42,757,6225,3650,9340,3219,742,8702,4166,1952,5381,9426,8575,5220,8197,5195,91,4490,4804,7486,7942,6518,7883,5379,685,3028,4855,5877,7828,8459,3269,860,7753,2034,8796,6831,7353,8299,4151,1039,5086,2172,8232,7809,3129,5104,9125,8557,9350,6608,8971,862,8828,4562,6322,4669,2421,7472,4592,6654,8187,4087,8536,6944,8671,5219,9818,2883,2595,2749}
Returns: 864611695
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Returns: 464090219
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002,8850,36,5003,9082,9568,8140,2333,8161,8648,2199,5316,1776,2408,3274,5755,7943,2818,1246,6710,4304,6800,229,9163,4822,5980,7509,9340,6686,6153,6494,9642,1832,4647,61,8021,3525,6969,4320,805,6647,6461,2004,6766,2094,7405,5473,4407,2390,2990,4084,1555,1801,8728,6573,4784,140,6395,4748,6283,2017,4629,4526,8417,4431,8774,8373,7305,7995,5371,1072,9360,5856,6434,4577,9513,9410,9528,8729,5787,5007,5836,4167,6371,5997,8967,7691,6900,1588,8641,7966,4202,5243,1780,1623,3289,5605,9861,6366,8027,5626,596,9434,7223,3619,2711,1433,6960,3949,1346,337,5284,6200,6478,624,3859,5495,4004,7954,3113,891,7070,589,6134,2840,587,6776,3582,7695,2203,1299,2572,6817,3686,471,7647,4476,4893,1566,4669,4298,4199,145,8288,1573,7548,2274,4939,4005,6440,2857,9955,4253,2807,9303,99,4555,7333,6278,1602,4742,4051,585,5062,2416,8060,8126,9127,2235,2126,915,2757,9484,3448,1204,3803,400,665,2319,9802,3231,4317,7434,5853,1418,9832,1456,2047,6807,6047,4263,4364,1604,7087,7588,4907,2009,1710,1870,4659,1680,5469,4696,3292,5479,2692,1969,2966,7576,518,3774,6542,1169,5161,681,4553,6221,3532,8294,1327,2874,6464,3254,9813,1458,3098,9831,4515,9238,881,3485,9494,3083,7926,9572,3485,7156,2112,6240,1853,6300,8456,3111,3610,6031,2926,9668,7858,208,5798,3499,605,2371,9729,7554,640,9645,606,6061,6287,2913,3871,3657,6071,3117,7453,3308,426,9575,8185,8945,2188,9051,5811,8552,8089,8074,7137,6079,3539,6107,2249,7037,6999,7188,3109,4415,2909,7388,1892,9106,4941,6381,4212,9841,4462,1512,4615,8691,8833,252,3958,9120,9798,4287,5597,5281,876,2365,2126,919,3304,1583,2468,3869,2202,8117,5837,3812,1889,2977,8164,3619,2839,5799,3795,8600,6976,4213,5446,9826,7700,3560,4460,9418,7726,4162,3881,1238,6157,9560,9313,4792,2074,447,687,6526,4955,8321,839,4554,7522,7718,4414,4255,7820,8549,7685,4088,3620,4257,7033,7409,7685,9918,3851,2184,5294,3206,9237,8331,8193,1370,130,4284,1963,5671,5993,4630,8873,6847,837,6067,8755,2774,2056,9052,9291,9757,6425,9310,1915,3130,7089,6067,2375,8448,1841,166,6817,4673,2431,5522,8677,8535,4462,7020,8613,3784,2104,5700,2487,5411,9499,1675,5696,2601,2546,1896,5604,1249,5073,1905,3859,6095,8204,2281,7791,7348,3166,4317,1140,7617,4263,2782,4358,8641,3964,9552,2741,6821,3320,1301,3991,5947,9031,9790,8398,7581,6838,3544,2653,8464,1820,5761,3037,9571,8915,5103,8178,7709,465,9036,1065,6578,2293,1977,8491,2929,6553,371,181,4126,2865,1161,3124,765,2111,5040,5459,9112,4594,9516,5694,2842,8027,1467,4654,1640,9414,6121,1897,1233,7367,3017,3215,9463,9060,6260,5652,8941,6815,7316,6813,4370,7661,5774,642,3277,5957,8709,2977,1960,2159,9872,5280,1272,2343,4495,1914,5499,6926,9130,7337,540,4862,8409,292,5993,726,9537,7378,2638,6885,4738,9763,9239,2445,5960,570,3328,2407,9522,3314,831,1779,2839,4826,8479,9468,4453,5437,3723,9081,3316,6394,3336,7662,7762,2035,4045,8378,9218,6099,1025,8882,1903,5429,799,9734,2348,7278,1266,694,4453,8659,7408,6274,4711,5234,378,3296,5544,3637,6307,5771,4992,4308,7160,7683,1208,7002,8336,9798,5624,9803,741,2183,2424,1808,2936,215,7600,7541,4022,4422,8890,9326,2291,9944,5884,2949,3959,2955,3991,8837,9336,2462,9049,4442,5078,5048,127,723,660,7738,5198,663,7903,771,6141,4312,2415,5478,4662,1638,3223,1981,6294,4395,1689,3663,7477,5858,3744,4577,4362,4192,5459,1632,5930,4931,2758,7780,4504,6641,6175,9878,5637,628,1240,7706,2086,6476,9711,7997,7661,7390,6797,2168,251,791,179,6833,1196,9844,2897,78,8102,207,9516,1998,4816,5941,1882,9600,3904,7621,6294,1062,2515,5211,6584,1188,599,973,442,7732,3838,7204,4816,107,6415,6050,2386,5950,1335,1289,1288,3646,3945,6199,5161,315,1416,8776,5376,1850,3631,9335,9029,4319,5312,6997,4280,2074,504,2145,9624,9438,9825,8443,8848,7524,692,2972,507,7745,248,5288,1347,2828,1776,8374,4355,7746,156,9255,7,7393,5874,3161,3007,529,7330,5668,81,3297,5840,9827,5337,2452,8478,8143,5825,1941,952,5046,8011,2327,1205,6662,6500,7675,7221,4964,7671,7697,1384,8545,4512,7405,8797,9995,3357,8687,9097,2679,1061,6155,9043,8834,299,313,2565,8230,9873,5426,6369,2794,7199,8396,210,5069,9152,769,7951,6255,8899,9039,9387,4646,6598,1404,7393,9315,7304,2137,8887,1690,3745,9360,2045,915,5549,8382,7685,7760,3969,6464,5718,4227,9259,7049,5877,4416,229,5979,2118,3505,5047,1781,7985,2499,5301,4912,1054,8960,7869,9156,5853,5254,97,3129,4922,8228,6143,4113,9941,524,1686,8778,2982,2007,3817,6800,4797,7260,6095,5234,3213,3187,3622,6881,6117,125,9804,258,9149,7006,7833,6946,7583,1953,2690,6294,1371,4559,1856,5428,6101,8842,9840,5870,4536,6542,1025,2869,6384,4318,3538,1000,5265,4321,745,5764,4994,8206,5886,2128,6748,2132,7527,1350,2452,9859,3160,9328,890,7782,5497,3891,516,3354,8917,8141,7793,5233,7483,6612,6174,4046,6624,4326,359,8837,6193,6057,6086,4819,7029,5142,527,6998,9451,483,3524,3500,9460,9193,7024,9242,1230,8876,3349,8564,2690,8883,8426,5246,5676,9245,1212,4243,2343,5527,1697,5501,2388,9361}
Returns: 782144103
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Returns: 981271981
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Returns: 784602497
64
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5,9985,2,3,9932,9960,9924,9917,9916,5,3,9920,3,9958,4,1,9944,2,1,9980,4,5,9996,5,9956,9917,3,9929,9903,4,9937,9972,1,9985,4,1,9994,9964,2,2,9929,5,2,9925,2,2,9923,3,9910,5,3,9983,4,5,9934,2,3,9956,1,5,9921,4,9984,1,3,9956,9970,1,3,9974,9903,4,9914,9963,5,9924,3,1,9959,9946,2,5,9974,2,1,9962,2,3,9925,4,9998,9967,9916,2,9962,4,1,9947,3,5,9920,1,4,9966,5,4,9904}
Returns: 228444824
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{5,1,4,1,5,2,3,4,5,5,2,3,1,5,1,1,3,2,4,4,5,4,1,4,2,1,4,5,5,5,3,5,4,2,3,2,3,2,4,3,4,4,2,3,5,3,4,4,3,4,4,3,5,3,4,1,1,1,4,1,2,5,3,2,1,3,4,5,5,2,2,4,1,4,2,2,4,3,2,1,4,3,5,1,4,1,5,1,2,1,3,4,3,4,1,4,2,4,4,5,3,5,4,3,3,4,2,4,4,5,5,1,2,3,2,4,3,3,5,1,1,5,3,4,3,3,1,2,4,2,1,5,3,2,4,5,4,4,4,1,1,1,4,2,5,1,3,5,4,4,1,5,2,4,4,3,1,2,1,2,3,1,2,5,3,4,3,4,2,3,3,4,1,2,2,2,5,3,4,4,3,4,3,1,5,3,5,5,3,5,5,1,4,5,4,1,2,4,5,2,5,1,4,2,3,3,1,1,4,5,5,1,5,1,1,3,4,2,1,5,2,5,3,1,5,4,1,2,4,3,2,3,4,5,5,4,5,1,2,1,1,2,4,1,1,4,2,4,4,4,3,2,5,5,2,2,1,2,3,5,4,4,5,5,3,1,2,1,5,1,3,1,5,4,5,2,3,5,4,3,4,3,2,2,1,1,4,5,4,5,4,2,4,3,5,1,4,5,5,2,3,5,5,3,5,3,3,4,1,4,1,3,5,4,2,3,2,2,3,5,3,4,5,1,1,3,3,1,4,4,5,3,1,1,4,1,4,5,2,3,3,2,4,4,3,1,5,2,4,4,5,4,5,3,1,1,4,2,2,1,2,1,2,3,2,4,2,1,1,4,1,4,4,4,3,4,1,4,1,4,5,3,2,4,1,3,3,5,2,2,4,3,5,5,3,4,3,1,4,4,2,3,5,4,1,4,2,1,3,3,4,3,3,2,1,1,4,4,3,3,3,1,1,3,1,1,5,1,3,5,3,3,1,1,5,5,5,4,1,1,1,3,4,1,4,3,1,1,2,1,5,4,2,1,2,2,5,5,4,1,4,2,2,1,3,1,3,5,1,3,5,5,3,2,5,4,1,2,1,1,3,5,1,4,1,2,5,4,1,2,3,2,3,2,1,1,4,3,3,4,4,3,3,1,4,2,3,2,5,1,4,2,4,5,3,2,3,5,2,3,4,1,5,2,4,3,5,4,2,3,1,4,4,2,5,4,2,2,3,4,5,4,1,2,2,5,2,2,2,3,3,1,1,3,2,4,2,2,1,5,4,4,1,5,2,4,5,3,1,4,4,3,2,1,2,1,5,3,4,5,2,5,5,1,3,3,3,4,2,3,5,3,3,4,3,4,5,1,4,1,3,4,1,1,1,2,1,1,5,4,5,5,4,3,4,5,5,3,2,3,5,1,2,5,4,1,1,3,1,2,4,5,2,5,3,1,4,5,1,3,5,3,1,1,3,5,2,3,5,1,1,2,1,2,1,1,3,2,5,2,4,4,4,3,5,5,1,3,2,1,1,1,3,4,4,1,1,5,1,3,2,5,5,1,2,5,1,5,5,2,3,3,3,1,5,3,1,5,1,4,3,1,3,1,4,5,5,5,4,4,2,5,5,3,1,2,1,2,4,1,4,2,2,1,1,5,2,5,4,3,1,5,1,1,1,2,5,4,5,2,2,4,2,5,4,2,5,4,5,3,1,3,1,5,2,5,4,3,2,1,3,3,4,1,5,4,2,1,3,5,1,4,2,3,2,4,4,4,4,1,4,3,5,3,3,3,4,2,3,4,5,5,1,4,1,4,4,3,2,1,5,1,5,5,2,4,4,2,2,1,1,4,3,4,5,2,3,3,2,4,4,4,2,2,5,3,4,3,4,2,4,5,3,3,2,2,5,5,1,2,4,2,5,2,4,3,4,4,2,1,2,2,1,1,2,4,2,4,2,2,5,5,2,3,3,5,5,5,1,2,2,1,3,3,4,4,2,1,5,5,1,3,1,2,3,4,3,2,5,1,1,1,1,1,3,5,4,5,3,4,2,4,2,4,5,4,4,4,2,4,4,5,2,2,5,4,5,2,3,3,5,1,4,5,3,2,4,5,3,5,4,5,5,4,4,4,1,4,2,4,2,4,4,5,3,3,2,1,5,2,1,3,1,4,2,3,5,1,5,3,1,2,3,2,5,2,5,2,2,2,4,3,3,5,1,5,2,2,4,1,5,1,3,1,1,2,5,1,2,3,2,5,1,2,2,3,1,1,4,1,3,4,3,4,4,3,2,4,1,5,5,3,2,5,9940,4,9908,9970,2,9978,1,9966,5,9932,9934,9921,2,2,9909,4,9917,5,10000,1,9928,9932,9954,4,9963,5,3,9959,1,4,9930,2,9957,4,2,9934,9984,5,4,9959,9917,9973,5,1,9910,4,9972,5,1,9971,9946,1,1,9928,2,9939,10000,9954,9923,2,1,9984,9921,9987,9908,9951,9911,9930,5,2,9930,9927,4,9926,2,9988,5,1,9989,1,3,9930,3,5,9911,5,1,9945,9940,5,4,9954,9935,9917,9970,1,1,9986,9972,2,9952,9942,9961,9953,9900,9914,2,3,9959,2,3,9995,2,5,9924,3,3,9968,5,9930,3,9976,5,9928,9914,2,9914,4,2,9989,5,9940,3,1,9940,2,1,9942,5,9901,1,9956,2,9981,9974,1,9970,9999,5,4,9970,9982,9952,9956,4,9909,4,1,9964,4,9935,4,9999,1,9930,9990,1,4,9914,9986,9967,9957,2,9934,9935,9999,2,3,9908,2,9948,3,9910,9929,3,1,9936,3,2,9969,9954,4,4,9934,1,5,9985,9918,5,5,9976,3,9976,3,9938,9915,9921,3,9909,1,2,9937,3,5,9938,9917,4,9973,9915,9944,9970,4,9910,9964,3,2,9984,1,9932,2,2,9929,2,9995,1,5,10000,2,1,9956,3,4,9923,5,5,9971,1,2,9983,5,3,9972,4,2,9911,3,1,9948,3,3,9926,3,9974,3,4,9952,1,9958,5,2,9968,2,4,9980,3,5,9944,5,9968,2,9987,4,9913,2,2,9940,9928,9964,5,9996,1,3,9998,1,5,9918,9901,4,9933,1,1,9934,2,9906,1,5,9992,2,9917,2,9901,1,1,9977,1,9977,5,5,9918,3,9916,1,9944,5,5,9971,1,2,9962,9946,9967,9962,2,9960,2,2,9961,1,9959,9981,4,2,9983,9968,5,9907,4,3,9977,4,2,9928,2,2,9901,5,5,9925,4,9974,9970,4,9944,9969,4,9905,2,9909,3,9994,9972,9967,3,3,9985,1,9996,5,3,9978,4,9942,1,2,9920,5,9989,9934,2,9980,1,9928,1,3,9951,4,9956,4,1,9991,2,3,9991,2,9971,9984,2,9920,9962,2,2,9901,9948,9951,9929,1,9999,9986,2,9946,5,1,9934,9913,4,3,9910,3,3,9965,1,9950,1,1,9986,9912,2,3,10000,3,2,9910,4,9960,9989,9945,9925,2,9919,3,5,10000,3,9938,9974,1,9978,9980,4,9901,3,9970,4,9925,4,9915,9946,5,9992,9920,9962,2,9948,2,9940,5,9983,3,1,9917,1,3,9974,5,9991,9921,2,3,9959,9956,9911,3,1,9909,1,1,9989,2,3,9911,9998,2,9981,5,3,9915,4,1,9936,9987,9933,9985,3,9926,5,9972,1,9964,1,2,9901,3,9967,4,2,9918,4,9970,5,9962,4,9940,4,2,9997,2,9942,9945,9925,1,9932,2,9912,1,3,9958,9995,5,5,9985,5,2,9972,4,5,9994,2,4,9920,4,9956,4,9906,5,9908,5,4,9947,2,9917,2,9922,9981,9959,9986,5,9995,9941,9931,3,4,9907,2,4,9904,2,9935,2,2,9977,9988,3,9962,4,9973,1,9981,9906,9985,4,9947,4,3,9961,1,9962,4,9956,5,9962,9976,9930,3,2,9992,9995,9973,9918,9932,9965,1,3,9935,4,2,9985,2,9908,2,9917,9948,4,4,9940,5,2,9997,2,9954,5,9996,9902,4,5,9904,3,2,9981,5,3,9930,4,4,9931,5,9943,9933,9956,9939,4,9933,1,9941,9943,1,9998,1,9974,1,3,9937,1,9978,9923,9984,9964,9973,1,9929,2,4,9900,9933,1,4,9920,9964,2,2,9933,9900,9973,4,9977,9953,4,3,9901,5,5,9909,5,4,9929,9970,9936,1,4,9996,2,3,9983,4,9999,2,9992,9937,9928,2,9959,2,9958,1,1,9975,2,9976,9922,9996,9990,5,9914,3,9989,4,4,9990,4,5,9989,2,2,9941,3,1,9999,2,9977,1,9972,9949,9933,4,9996,2,9933,2,9922,5,4,9990,4,1,9989,5,5,9915,4,9904,3,5,9927,9974,9939,1,1,9900,9939,4,2,9919,2,5,9995,2,9978,1,9961,9958,9969,9955,9921,9994,4,5,9971,9912,9917,2,9947,9939,1,2,9985,9965,5,9987,9992,2,4,9954,9943,9987,4,5,9900,9935,3,9965,3,9992,2,1,9940,4,9974,2,9984,5,5,9957,9933,3,9926,9986,5,4,9909,1,9907,2,9947,1,3,9916,9924,3,2,9971,9960,3,9986,9907,3,9921,4,4,9933,3,2,9914,3,4,9968,3,9918,4,9955,5,9935,3,9903,9934,5,4,9925,9954,2,9916,2,5,9909,9979,2,4,9957,2,9958,1,9915,1,9960,9995,4,4,9941,5,9993,1,10000,9980,9925,1,9957,9963,9977,5,9900,4,1,9993,2,9953,2,1,9982,3,1,9963,3,9993,2,9964,3,5,9981,3,9913,4,9968,9940,1,9942,4,3,9977,9928,9918,9984,9938,2,9905,5,4,9961,3,4,9910,9985,5,9914,3,9927,9980,9954,9909,2,9945,9980,9903,2,5,9922,4,5,9965,1,2,9946,4,9959,1,2,9952,5,4,9929,3,1,9958,5,9965,1,9973,9921}
Returns: 945310381
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1,9983,9946,3,4,9948,3,9945,3,9910,9965,2,3,9928,3,2,9947,4,9991,9914,9926,3,9987,1,9978,5,1,9924,9999,3,9911,1,1,9969,2,9986,3,9921,1,5,9946,5,4,9973,9940,2,9924,2,9996,4,9981,3,9911,1,9983,3,2,9912,9939,1,9964,3,2,9974,5,9928,3,9919,2,3,9907,9958,3,9968,1,4,9988,3,9965,9970,9972,1,5,9977,1,1,9982,5,9956,5,9932,9929,2,9989,9920,5,9959}
Returns: 870707463
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5,9908,9929,5,4,9971,4,9964,9900,9982,9914,9923,4,2,9956,3,4,9996,9960,2,2,9979,9947,1,4,9955,3,4,9972,9925,2,1,9955,5,4,9905,9972,3,9907,5,1,9925,9964,9953,9965,9954,9910,5,9912,5,5,9923,1,4,9928,9986,9941,3,5,9907,4,9988,5,9948,2,9908,9904,9930,9946,2,9924,9957,9951,4,9978,5,2,9912,4,4,9999,3,9957,3,3,9972,9971,9941,2,9941,4,9956,3,9981,5,10000,9951,9900,9980}
Returns: 329636287
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70,9999,3,9961,9970,9984,4,9993,2,5,9978,1,9986,4,1,9972,5,1,9946,9989,5,3,9988,2,4,9996,9905,9958,5,1,9923,9921,9934,9955,4,2,9998,4,1,9932,1,9905,4,5,9962,4,3,9917,9907,2,9961,5,9905,2,3,9925,1,1,9944,9982,2,9903,1,9912,9935,2,9974,3,9923,1,5,9986,9930}
Returns: 335896609
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,3,9922,2,4,9933,9921,9950,4,9984,5,9988,4,3,9920,4,3,9989,3,9967,9931,3,5,9937,2,3,9950,2,9978,9936,3,9987,5,1,9950,4,3,9913,3,3,9922,9955,9989,4,3,9990,1,1,9942,5,4,9972,2,1,9925,1,4,9928,1,3,9972,2,9907,9970,1,9920,9970,4,2,9930,9900,3,3,9950,3,1,9932,4,2,9988,5,4,9934,4,9987,2,3,9938,2,9959,2,9965,4,9988,9939,9922,3,2,9922,4,5,9956,9928,9923,2,2,9978,3,1,9996,3,5,9996,4,1,9957,9910,2,9985,9900,1,9983,4,1,9936,4,9983,9902,4,2,9983,4,9909,9969}
Returns: 803139321
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938,2,1,9959,9986,4,9958,3,3,9912,4,2,9946,3,9953,1,9927,5,3,9911,3,3,9913,4,9961,2,9980,2,9978,1,9993,9918,5,4,9983,9990,9993,5,9913,2,1,9934,3,5,9924,9931,4,4,9967,3,9996,3,9919,3,4,9979,9944,5,4,9930,1,1,9983,5,2,9983,9988,9970,2,9918,4,3,9992,9961,9913,4,9980,3,3,9943,9948,9952,1,9956,2,1,9991,9940,9951,3,1,9934,3,9934,3,9954,4,4,9941,9916,9950,9973,4,9934,9909,5,1,9948,4,9945,5,10000,9978,3,9968,1,3,9989}
Returns: 128911751
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4,2,9913,3,9934,9944,4,9972,9996,1,9996,4,4,9926,9922,2,2,9995,2,1,9975,5,9997,5,1,9971,1,9905,1,9913,9901,4,5,9994,1,3,9934,4,9951,2,1,9947,4,9921,2,9925,3,3,9954,1,1,9957,5,1,9950,9972,9945,9900,9901,3,4,9930,2,2,9947}
Returns: 894605653
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,9969,1,9967,3,1,9988,9984,2,9928,9980,10000,9976,3,4,9932,2,9931,9948,2,1,9945,5,9927,2,9955,2,9929,4,5,9977,4,9950,9966,9981,1,3,9920,1,5,9941,3,2,9902,5,9929,1,2,9989,5,9946,5,2,9962,5,9943,4,9931,9918,3,4,9978,9982,9986,1,9964,2,4,9994,1,4,9979,5,9995,9969,9994,5,9983,9956,4,4,9984,2,1,9955,9952,9978,2,9969,5,9962,9925,2,9960,1,9949,9911,4,9911,9951,1,9949,3,2,9956,9988}
Returns: 700361071
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2,3,9938,1,4,9990,9982,1,4,9992,9945,3,9943,5,1,9960,3,1,9913,9970,3,3,9937,3,9941,9911,2,4,9957,3,9969,5,9950,5,5,9916,9953,2,1,9981,5,2,9992,2,3,9959,5,9971,9964,3,5,9924,5,5,9917,4,2,9918,9913,5,9911,3,4,9953,1,5,9927,5,9938,9904,9992,3,4,9911,1,9911,2,9948,2,10000,3,2,9974,5,9990,3,9913,2,1,9990,9948,2,1,9983,9963,9972}
Returns: 102958513
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9986,2,9959,9960,4,9957,4,4,9935,2,2,9998,9979,5,9916,4,9974,4,2,9952,5,5,9905,1,9975,1,9919,4,2,9977,2,9934,5,4,9967,4,9931,2,9964,5,9959,9939,2,9995,4,9965,3,1,9920,5,1,9986,1,3,9936,2,9931,9963,9915,3,1,9966,4,3,9909,1,1,9985,4,1,9933,9973,9953,5,3,9971,2,4,9947,5,9908}
Returns: 979988396
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2,10000,9933,3,9908,9907,3,4,9903,9909,4,9925,9999,9904,4,9960,4,9909,1,3,9964,9918,1,9906,5,3,9986,9904,1,9917,2,5,9900,10000,3,9957,1,1,9917,9981,4,4,9984,9920,4,9975,3,9991,2,5,9916,1,9947,1,3,9976,9970,9943,4,1,9943,4,2,9955,2,9983,9956,1,3,9972,1,3,9971,9989,1,9925,3,1,9940,5,9923}
Returns: 652534516
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967,4,2,9915,9938,4,9953,4,1,9946,5,9924,3,9977,1,9963,5,3,9997,9969,9941,9998,9965,9939,3,9954,9900,5,9923,9904,9965,9943,4,3,9991,9937,5,9944,9993,4,1,9933,2,9908,2,9901,9968,1,3,9951,1,2,9991,5,5,9967,5,9927,9900,3,9992,3,9967,4,9900,1,1,9928,9932,2,9908,9969,9902,5,5,9902,2,2,9900,2,9958,2,2,9950,2,10000,2,4,9943,9979,3,3,9973,9977,4,5,9917,3,9972,9938,2,9911,9960}
Returns: 618370150
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Returns: 281023517
{0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45, 45, 46, 46, 47, 47, 48, 48, 49, 49, 50, 50, 51, 51, 52, 52, 53, 53, 54, 54, 55, 55, 56, 56, 57, 57, 58, 58, 59, 59, 60, 60, 61, 61, 62, 62, 63, 63, 64, 64, 65, 65, 66, 66, 67, 67, 68, 68, 69, 69, 70, 70, 71, 71, 72, 72, 73, 73, 74, 74, 75, 75, 76, 76, 77, 77, 78, 78, 79, 79, 80, 80, 81, 81, 82, 82, 83, 83, 84, 84, 85, 85, 86, 86, 87, 87, 88, 88, 89, 89, 90, 90, 91, 91, 92, 92, 93, 93, 94, 94, 95, 95, 96, 96, 97, 97, 98, 98, 99, 99, 100, 100, 101, 101, 102, 102, 103, 103, 104, 104, 105, 105, 106, 106, 107, 107, 108, 108, 109, 109, 110, 110, 111, 111, 112, 112, 113, 113, 114, 114, 115, 115, 116, 116, 117, 117, 118, 118, 119, 119, 120, 120, 121, 121, 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}
Returns: 591531325
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1003, 4081, 8907, 4486, 3492, 6990, 9175, 1545, 8657, 8389, 162, 3971, 2739, 5842, 3103, 1380, 6849, 1019, 3767, 839, 4043, 251, 2943, 4285, 960, 8489, 4462, 5136, 2597, 8925, 1207, 3599, 9357, 114, 4436, 2848, 3455, 9963, 745, 2111, 4703, 7258, 2433, 7441, 9452, 1887, 5172, 6300, 2905, 5290, 3490, 6947, 5540, 2785, 7583, 2851, 1273, 2044, 7987, 3869, 7320, 9193, 3819, 6677, 5658, 8254, 5876, 5464, 8216, 6620, 3926, 9270, 3878, 2710, 6710, 9681, 4596, 8233, 2332, 7501, 3523, 5821, 4447, 5414, 4957, 2030, 8265, 6229, 425, 6251, 6449, 7745, 1795, 6619, 773, 3805, 4873, 6648, 9268, 9440, 9620, 3194, 8710, 9849, 2255, 1771, 9529, 6851, 6356, 1860, 4351, 6230, 4032, 5149, 1643, 8989, 7178, 9907, 1569, 3955, 2509, 4370, 1699, 4304, 988, 2471, 8108, 2212, 5470, 3727, 8004, 1441, 3272, 3065, 1289, 5527, 1187, 817, 2377, 7542, 9028, 3079, 123, 3060, 8227, 1766, 8400, 5405, 8024, 9968, 9359, 533, 689, 7409, 1188, 1677, 6231, 9295, 240, 8052, 9373, 8243, 9493, 2645, 1307, 781, 4523, 2494, 7950, 6899, 6387, 3329, 9977, 6510, 6388, 8203, 4627, 1139, 9959, 2650, 7459, 5669, 3182, 8147, 9429, 721, 6175, 5659, 15, 6415, 63, 5740, 4657, 9555, 4736, 2316, 335, 9258, 1161, 4636, 2508, 7547, 7965, 2484, 4056, 704, 7038, 5034, 1843, 3349, 7684, 9301, 5369, 7217, 7447, 1150, 7938, 3622, 3160, 4304, 6388, 3222, 43, 1044, 2776, 4778, 9711, 9463, 387, 871, 4098, 2894, 8418, 2062, 1729, 8825, 9118, 8767, 3859, 960, 8467, 7894, 260, 187, 5110, 4058, 1336, 3047, 4031, 4496, 3703, 418, 7717, 97, 7814, 493, 4875, 7524, 6307, 5261, 8395, 404, 4507, 3164, 8818, 6235, 8340, 7935, 1353, 8550, 8894, 9819, 6443, 5505, 6, 7905, 5914, 7693, 7303, 9945, 2188, 1005, 362, 6257, 1102, 4527, 6749, 2328, 2051, 3055, 3940, 6797, 9810, 8446, 6312, 8627, 4681, 1003, 2913, 6033, 9553, 8158, 2204, 2347, 3662, 8561, 251, 5928, 6253, 7554, 5872, 8441, 8558, 2585, 1049, 6011, 7112, 4149, 8338, 5514, 3555, 2278, 8662, 3364, 7075, 1325, 8343, 1755, 2327, 1255, 4140, 1879, 5765, 6343, 4226, 5778, 4903, 828, 1705, 1155, 8381, 7576, 5947, 3291, 161, 6995, 9301, 3624, 1143, 3991, 5489, 4697, 2620, 4150, 4413, 9694, 1826, 2755, 1449, 4152, 361, 5588, 2383, 6125, 1930, 2960, 1903, 3184, 3787, 3607, 4338, 2168, 7535, 6637, 1810, 4047, 3631, 1110, 7670, 1126, 1452, 3158, 2174, 4071, 3659, 6586, 3765, 5484, 9340, 1565, 5987, 6053, 3504, 8369, 2177, 5433, 1328, 431, 4968, 1467, 4038, 9305, 3634, 1572, 2293, 1795, 5618, 2276, 9256, 9639, 3401, 708, 9148, 5574, 4778, 9158, 2160, 4894, 993, 7851, 6458, 6979, 3903, 9961, 5348, 2432, 1745, 3027, 2862, 6712, 4493, 6899, 2369, 4478, 4822, 4661, 6272, 6791, 3288, 1880, 2781, 6688, 2587, 8280, 8614, 7364, 7437, 7125, 8610, 8429, 4975, 5067, 1760, 5230, 5028, 3459, 7661, 6772, 6485, 6874, 9836, 7330, 125, 2204, 8159, 4946, 3216, 783, 8089, 6504, 2662, 869, 9543, 5248, 5501, 8156, 8963, 2937, 1632, 7572, 7718, 2959, 2639, 9477, 8188, 4018, 2935, 2200, 7141, 5771, 9073, 3328, 9452, 9197, 1883, 7611, 495, 5099, 8393, 8583, 7954, 1054, 5803, 3848, 2653, 7655, 8356, 1615, 592, 9987, 5539, 4661, 2945, 4529, 489, 7484, 8546, 3423, 6035, 2038, 5545, 5108, 5366, 4997, 656, 7248, 2607, 1150, 8698, 7351, 6084, 3003, 8404, 8239, 6851, 1056, 5893, 5206, 9022, 2836, 5192, 912, 7496, 4489, 5440, 7984, 8324, 337, 7758, 4359, 8727, 3303, 9466, 4092, 4651, 121, 7691, 3609, 7623, 6389, 959, 58, 9391, 9362, 8296, 6241, 6769, 541, 7798, 2142, 3376, 9342, 3054, 7224, 3830, 4845, 1559, 2153, 1534, 9317, 6511, 260, 8971, 2328, 4351, 9973, 8801, 2041, 3581, 2775, 4781, 4539, 2832, 4172, 3900, 7480, 6764, 7020, 8020, 4562, 5513, 7747, 255, 4918, 4970, 4084, 9763, 6529, 2588, 1296, 2197, 5451, 1555, 1167, 4130, 2257, 1139, 2930, 4297, 4719, 2056, 5430, 5609, 4888, 9601, 9508, 8719, 2716, 2879, 6738, 3629, 8391, 836, 3883, 3309, 5806, 4318, 9423, 8686, 3258, 7070, 882, 8708, 8624, 8400, 2837, 880, 5890, 2119, 1528, 608, 4174, 6957, 6216, 5413, 2909, 2075, 4131, 1977, 1305, 7220, 1957, 6047, 8056, 5840, 5707, 213, 6509, 5129, 8898, 9766, 2198, 6131, 8473, 7173, 4530, 7662, 4404, 419, 6132, 2284, 7378, 6657, 5592, 9945, 2070, 4853, 8371, 2552, 6829, 6027, 6124, 8785, 2073, 531, 976, 7780, 7095, 7485, 9260, 5992, 7250, 7810, 8474, 2075, 4982, 3003, 9736, 5738, 9773, 5867, 8021, 3502, 8875, 3612, 3446, 944, 4816, 8168, 9848, 1644, 4194, 2323, 6781, 2618, 9205, 4108, 397, 6299, 1592, 6009, 2290, 5194, 3818, 763, 7268, 5151, 117, 3355, 888, 6241, 5573, 5260, 9742, 4447, 5224, 9539, 1743, 39, 7706, 1590, 1683, 8251, 264, 4815, 868, 9468, 8922, 7617, 5766, 6866, 3625, 4407, 2059, 7442, 1521, 9326, 2592, 7989, 2680, 9832, 4229, 8252, 5091, 3970, 2698, 314, 9860, 792, 353, 3917, 8733, 8387, 2167, 8996, 3201, 9386, 4815, 8474, 7002, 580, 5339, 6978, 1338, 7397, 4419, 2858, 3074, 3363, 846, 2105, 3194, 1426, 6708, 4636, 1747, 9406, 4950, 1606, 6549, 1654, 1874, 5282, 40, 4040, 4277, 9592, 9778, 9092, 8065, 3131, 6023, 9756, 109, 7361, 7152, 4527, 6570, 6578, 4241, 7416, 8682, 7434, 5193, 5390, 2070, 6940, 1147, 3371, 4897, 7695, 5024, 6771, 2976, 1415, 7162, 3605, 1006, 6939, 2696, 5422, 70, 5070, 5177, 178, 2430, 8681, 1056, 9000, 5258, 5297, 2767, 3939, 9082, 7959, 5680, 7503, 1250, 6826, 7225, 6147, 873, 2248, 2917, 3848, 3662, 78, 7452, 1019, 7017, 6499, 6441, 3438, 1569, 1617, 9967, 350, 297, 1022, 9349, 1906, 2670, 8467, 2197, 1752, 2778, 7876, 5606, 4027, 1054, 2831, 173, 1926, 1430, 3089, 5773, 1444, 9519, 9577, 2462, 2887, 2427, 8902, 6324, 3995, 6871, 6290, 697, 3519, 3663, 6397, 5425, 6333, 4864, 7621, 4436, 7641, 1848, 6393, 8019, 2901, 9223, 4544, 4826, 7005, 3984, 6951, 8448, 3502, 2879, 909, 6388, 5305, 6163, 9063, 5652, 3033, 5352, 6348, 2903, 5367, 2744, 8327, 8051, 3959, 2299, 8838, 7951, 499, 5230, 5970, 3399, 805, 513, 4577, 7809, 848, 7879, 6256, 4350, 7109, 7164, 737, 8765, 9678, 6152, 4416, 2710, 7855, 7115, 5613, 3221, 6211, 291, 1271, 169, 8942, 108, 4472, 9440, 1690, 441, 9190, 2494, 7305, 118, 6654, 8152, 4348, 2909, 8853, 1456, 6424, 5942, 6573, 6102, 2093, 7340, 5163, 9947, 4455, 7127, 9520, 7017, 3770, 790, 7185, 2711, 7250, 1656, 8502, 5291, 8448, 4043, 7784, 2104, 513, 789, 6608, 1212, 3697, 1812, 9020, 6472, 7753, 5592, 8925, 6197, 2931, 4088, 6144, 3737, 7566, 5663, 753, 1335, 2804, 4290, 397, 6405, 2297, 8898, 1695, 7097, 9293, 5830, 9200, 6157, 6618, 2159, 7368, 6666, 323, 6387, 3138, 8075, 1978, 2062, 4272, 4909, 2501, 6767, 4997, 67, 8781, 5750, 1401, 7936, 39, 1798, 4341, 2335, 7047, 2387, 9431, 2691, 8217, 4983, 8847, 1186, 3493, 6215, 7852, 3815, 8953, 7341, 8242, 931, 5754, 8865, 2191, 8255, 5631, 7187, 4673, 763, 9288, 6073, 8698, 9326, 4222, 9390, 1661, 7621, 1777, 7443, 311, 9993, 2425, 5510, 7530, 2270, 8076, 5381, 6084, 7028, 2721, 4325, 4310, 8475, 3189, 6500, 3081, 5171, 39, 7753, 5933, 9326, 177, 983, 8652, 4399, 372, 6664, 8371, 2148, 458, 5033, 8492, 9235, 542, 6022, 1504, 8617, 7754, 3939, 1997, 6827, 8264, 6306, 1653, 7804, 9158, 4733, 9327, 9196, 8837, 5259, 8521, 9013, 2593, 3524, 9763, 2965, 6539, 8133, 1464, 3349, 3166, 6308, 2583, 59, 2329, 438, 5028, 6434, 4376, 7024, 3260, 8991, 3329, 4912, 3147, 2486, 5996, 2473, 8033, 4832, 4083, 2906, 197, 6676, 6429, 9959, 9640, 9320, 4444, 7455, 2668, 3961, 3762, 1602, 371, 2442, 2039, 5398, 8876, 6414, 2421, 8487, 1757, 2102, 3399, 4903, 939, 5746, 7375, 5324, 6930, 1457, 8229, 7126, 8132, 1009, 3436, 4123, 6680, 4231, 1578, 9347, 8191, 1691, 948, 4914, 4133, 9338, 311, 3008, 5752, 9084, 1494, 7508, 7537, 1244, 2410, 4827, 6990, 6136, 150, 3919, 7592, 8378, 7396, 5724, 5739, 831, 6198, 2418, 1414, 7775, 8117, 5956, 9466, 5416, 869, 9950, 4754, 1180, 2957, 6857, 6615, 802, 716, 4151, 8398, 9477, 8977, 1739, 5612, 9127, 2009, 3203, 3856, 9404, 5278, 9594, 6586, 1476, 2012, 7999, 5602, 128, 307, 1419, 5543, 1175, 1368, 6648, 2354, 4324, 3504, 8968, 1478, 4219, 9470, 6227, 3695, 8447, 7965, 9306, 3925, 9973, 8861, 7780, 5728, 4138, 3726, 8665, 1965, 5737, 3016, 7567, 2216, 3322, 8985, 4110, 4496, 353, 758, 3202, 1028, 4261, 8521, 8857, 4832, 7991, 5083, 8526, 2789, 3047, 4184, 6713, 9371, 3044, 4492, 1450, 3533, 8217, 6467, 5498, 305, 9482, 3064, 8872, 9155, 8400, 2982, 2, 8752, 91, 3203, 6132, 703, 8076, 4988, 5534, 6066, 71, 412, 5206, 9469, 947, 1918, 5192, 3990, 2761, 2993, 3874, 7330, 9459, 9371, 7634, 5292, 8786, 2858, 798, 3538, 2191, 800, 2289, 2281, 354, 4772, 9335, 8429, 9760, 1221, 846, 6182, 7984, 6051, 2002, 8930, 4320, 7193, 9271, 7081, 6538, 3144, 4410, 2348, 8867, 8395, 7640, 4004, 7604, 4789, 7541, 9794, 5588, 6182, 8426, 5942, 953, 4113, 722, 7064, 5333, 1568, 3245, 3316, 3970, 5247, 2245, 8290, 8791, 1515, 1722, 5328, 1010, 6131, 7676, 9876, 877, 1667, 232, 8481, 6455, 7772, 4626, 2043, 305, 9404, 4336, 1258, 3516, 5057, 4673, 8848, 2976, 7918, 8515, 6946, 3164, 759, 1587, 1954, 8625, 3308, 7282, 9634, 5790, 1309, 5862, 3018, 2975, 6093, 7850, 9429 }
Returns: 148070238