Problem Statement
Given an array A[0..n-1], an inversion is a pair of indices (i, j) such that i < j but A[i] > A[j].
Inversions are a measure of how sorted the array is. For example, an array of n distinct elements has no inversions at all when sorted in ascending order and the maximum number of inversions when sorted in descending order.
A string can be seen as an array of characters. And as we can compare characters, we can extend the definition of inversions to strings.
For example, the string S = "hello" can be seen as the array S = { 'h', 'e', 'l', 'l', 'o' }. The pair (0, 1) is an inversion because 0 < 1 while S[0] > S[1]. The pairs (0, 2) and (2, 3) are not inversions: in the first case 'h' < 'l' and in the second case 'l' = 'l'. In fact, (0, 1) is the only inversion for this particular string.
You are given the length L and the desired number of inversions N. We are interested in strings of length L that consist of lowercase English letters ('a'-'z') only. Determine whether one of those strings contains exactly N inversions. If yes, return any one such string. If no, return the empty string instead.
Definition
- Class:
- Stringversions
- Method:
- create
- Parameters:
- int, int
- Returns:
- String
- Method signature:
- String create(int L, int N)
- (be sure your method is public)
Constraints
- L will be between 1 and 500, inclusive.
- N will be between 0 and L*(L-1)/2, inclusive.
Examples
5
1
Returns: "hello"
We want a string of length 5 with exactly 1 inversion. As we saw in the problem statement, "hello" is one of many different strings with this property.
7
0
Returns: "xxxxxxx"
We want a string of length 7 with no inversions at all. As shown by our example answer, a string with seven identical characters has this property. The string "pqrstxy" would also be an acceptable answer. The string "billowy" is probably the only meaningful 7-letter English word with this property.
7
21
Returns: "sponged"
This is the maximum number of inversions a string of length 7 can have. Among valid English words the strings "sponged" and "wronged" have this property, but you can also return any other meaningless string with 21 inversions.
27
351
Returns: ""
There are some arrays of length 27 with exactly 351 inversions. However, there is no string of 27 lowercase English letters with this property. (There are some strings of length 27 with 350 inversions.)
1
0
Returns: "z"
2
0
Returns: "yz"
2
1
Returns: "zy"
500
0
Returns: "aaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbcccccccccccccccccccdddddddddddddddddddeeeeeeeeeeeeeeeeeeefffffffffffffffffffggggggggggggggggggghhhhhhhhhhhhhhhhhhhiiiiiiiiiiiiiiiiiiijjjjjjjjjjjjjjjjjjjkkkkkkkkkkkkkkkkkkklllllllllllllllllllmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnooooooooooooooooooopppppppppppppppppppqqqqqqqqqqqqqqqqqqqrrrrrrrrrrrrrrrrrrrssssssssssssssssssstttttttttttttttttttuuuuuuuuuuuuuuuuuuuuvvvvvvvvvvvvvvvvvvvvwwwwwwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyzzzzzzzzzzzzzzzzzzzz"
500
120190
Returns: "zzzzzzzzzzzzzzzzzzzzyyyyyyyyyyyyyyyyyyyyxxxxxxxxxxxxxxxxxxxxwwwwwwwwwwwwwwwwwwwwvvvvvvvvvvvvvvvvvvvvuuuuuuuuuuuuuuuuuuuutttttttttttttttttttsssssssssssssssssssrrrrrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqqpppppppppppppppppppooooooooooooooooooonnnnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmlllllllllllllllllllkkkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhgggggggggggggggggggfffffffffffffffffffeeeeeeeeeeeeeeeeeeedddddddddddddddddddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaa"
500
120191
Returns: ""
25
152
Returns: "topcoderroundonesubroundb"
36
620
Returns: "zzyyxxwwvvuuttssrrqqponmlkjihgfedcba"
36
621
Returns: ""
122
7153
Returns: "zzzzzyyyyyxxxxxwwwwwvvvvvuuuuutttttsssssrrrrrqqqqqpppppooooonnnnnmmmmmlllllkkkkkjjjjjiiiiihhhhggggffffeeeeddddccccbbbbaaaa"
122
7154
Returns: ""
48
1106
Returns: "zzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeedcba"
48
1107
Returns: ""
453
98655
Returns: "zzzzzzzzzzzzzzzzzzyyyyyyyyyyyyyyyyyyxxxxxxxxxxxxxxxxxxwwwwwwwwwwwwwwwwwwvvvvvvvvvvvvvvvvvvuuuuuuuuuuuuuuuuuuttttttttttttttttttssssssssssssssssssrrrrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqppppppppppppppppppooooooooooooooooonnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmlllllllllllllllllkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhgggggggggggggggggfffffffffffffffffeeeeeeeeeeeeeeeeedddddddddddddddddcccccccccccccccccbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaa"
453
98656
Returns: ""
69
2286
Returns: "zzzyyyxxxwwwvvvuuutttsssrrrqqqpppooonnnmmmlllkkkjjjiihhggffeeddccbbaa"
69
2287
Returns: ""
67
2155
Returns: "zzzyyyxxxwwwvvvuuutttsssrrrqqqpppooonnnmmmlllkkjjiihhggffeeddccbbaa"
67
2156
Returns: ""
2
1
Returns: "zy"
31
460
Returns: "zzyyxxwwvvutsrqponmlkjihgfedcba"
31
461
Returns: ""
260
32500
Returns: "zzzzzzzzzzyyyyyyyyyyxxxxxxxxxxwwwwwwwwwwvvvvvvvvvvuuuuuuuuuuttttttttttssssssssssrrrrrrrrrrqqqqqqqqqqppppppppppoooooooooonnnnnnnnnnmmmmmmmmmmllllllllllkkkkkkkkkkjjjjjjjjjjiiiiiiiiiihhhhhhhhhhggggggggggffffffffffeeeeeeeeeeddddddddddccccccccccbbbbbbbbbbaaaaaaaaaa"
260
32501
Returns: ""
59
1671
Returns: "zzzyyyxxxwwwvvvuuutttssrrqqppoonnmmllkkjjiihhggffeeddccbbaa"
59
1672
Returns: ""
11
55
Returns: "zyxwvutsrqp"
439
92653
Returns: "zzzzzzzzzzzzzzzzzyyyyyyyyyyyyyyyyyxxxxxxxxxxxxxxxxxwwwwwwwwwwwwwwwwwvvvvvvvvvvvvvvvvvuuuuuuuuuuuuuuuuutttttttttttttttttsssssssssssssssssrrrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqpppppppppppppppppooooooooooooooooonnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmlllllllllllllllllkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhgggggggggggggggggfffffffffffffffffeeeeeeeeeeeeeeeeedddddddddddddddddccccccccccccccccbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaa"
439
92654
Returns: ""
189
17171
Returns: "zzzzzzzzyyyyyyyyxxxxxxxxwwwwwwwwvvvvvvvvuuuuuuuuttttttttsssssssrrrrrrrqqqqqqqpppppppooooooonnnnnnnmmmmmmmlllllllkkkkkkkjjjjjjjiiiiiiihhhhhhhgggggggfffffffeeeeeeedddddddcccccccbbbbbbbaaaaaaa"
189
17172
Returns: ""
1
0
Returns: "z"
53
1350
Returns: "zzzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeddccbbaa"
53
1351
Returns: ""
356
60928
Returns: "zzzzzzzzzzzzzzyyyyyyyyyyyyyyxxxxxxxxxxxxxxwwwwwwwwwwwwwwvvvvvvvvvvvvvvuuuuuuuuuuuuuuttttttttttttttssssssssssssssrrrrrrrrrrrrrrqqqqqqqqqqqqqqppppppppppppppoooooooooooooonnnnnnnnnnnnnnmmmmmmmmmmmmmmllllllllllllllkkkkkkkkkkkkkkjjjjjjjjjjjjjjiiiiiiiiiiiiiihhhhhhhhhhhhhgggggggggggggfffffffffffffeeeeeeeeeeeeedddddddddddddcccccccccccccbbbbbbbbbbbbbaaaaaaaaaaaaa"
356
60929
Returns: ""
8
28
Returns: "zyxwvuts"
6
15
Returns: "zyxwvu"
3
3
Returns: "zyx"
96
4428
Returns: "zzzzyyyyxxxxwwwwvvvvuuuuttttssssrrrrqqqqppppoooonnnnmmmmllllkkkkjjjjiiiihhhgggfffeeedddcccbbbaaa"
96
4429
Returns: ""
36
440
Returns: "qqrrssttuuvvwwxxyyzzponmlkjihgfedcba"
488
74814
Returns: "kkkkkklllllllllllllllllllmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnooooooooooooooooooopppppppppppppppppppqqqqqqqqqqqqqqqqqqqrrrrrrrrrrrrrrrrrrrssssssssssssssssssstttttttttttttttttttuuuuuuuuuuuuuuuuuuuvvvvvvvvvvvvvvvvvvvwwwwwwwwwwwwwwwkwwwwxxxxxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyzzzzzzzzzzzzzzzzzzzkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhgggggggggggggggggggffffffffffffffffffeeeeeeeeeeeeeeeeeeddddddddddddddddddccccccccccccccccccbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaa"
48
1049
Returns: "uvvwuwxxyyzzttssrrqqppoonnmmllkkjjiihhggffeedcba"
114
5042
Returns: "pqqqqqrrrrrssssstttttuupuuuvvvvvwwwwwxxxxxyyyyyzzzzzppoooonnnnmmmmllllkkkkjjjjiiiihhhhggggffffeeeeddddccccbbbbaaaa"
1
0
Returns: "z"
2
1
Returns: "zy"
130
7515
Returns: "sstttttuuuuuvvvvvwwwwwsxxxxxyyyyyzzzzzssrrrrrqqqqqpppppooooonnnnnmmmmmlllllkkkkkjjjjjiiiiihhhhhgggggfffffeeeeedddddcccccbbbbbaaaaa"
59
471
Returns: "effgghhiijjkkllmmnnooppqqrrsstttuuuvvvwwewxxxyyyzzzddccbbaa"
13
56
Returns: "tuvwxyszrqpon"
8
17
Returns: "vwxyuzts"
54
1230
Returns: "rssttuurvvwwxxyyyzzzqqppoonnmmllkkjjiihhggffeeddccbbaa"
44
244
Returns: "hgiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzfedcba"
1
0
Returns: "z"
3
3
Returns: "zyx"
385
12726
Returns: "ccccccddddddddddddddeeeeeeeeeeeeeefffffffffffffffggggggggggggggghhhhhhhhhhhhhhhiiiiiiiiiiiiiiijjjjjjjjjjjjjjjkkkkkkkkkkkkkkklllllllllllllllcmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnooooooooooooooopppppppppppppppqqqqqqqqqqqqqqqrrrrrrrrrrrrrrrssssssssssssssstttttttttttttttuuuuuuuuuuuuuuuvvvvvvvvvvvvvvvwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyzzzzzzzzzzzzzzzcccccccbbbbbbbbbbbbbbaaaaaaaaaaaaaa"
13
27
Returns: "qrstpuvwxyzon"
156
6826
Returns: "jjjjjkkkkkkllllllmmmmmmnnnnjnnooooooppppppqqqqqqrrrrrrssssssttttttuuuuuuvvvvvvwwwwwwxxxxxxyyyyyyzzzzzziiiiiihhhhhhggggggffffffeeeeeeddddddccccccbbbbbbaaaaaa"
50
489
Returns: "hhiijjkkllgmmnnooppqqrrssttuuvvwwxxyyzzgffeeddccba"
389
46785
Returns: "kkkkkkkkkklllllllllllllllmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnooooooooooooooopppppppppppppppqqqqqqqqqqqqqqqrrrrrrrrrrrrrrrssssssssssssssstttttttttttttttkuuuuuuuuuuuuuuuvvvvvvvvvvvvvvvwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyzzzzzzzzzzzzzzzkkkkjjjjjjjjjjjjjjjiiiiiiiiiiiiiiihhhhhhhhhhhhhhhgggggggggggggggfffffffffffffffeeeeeeeeeeeeeeedddddddddddddddcccccccccccccccbbbbbbbbbbbbbbbaaaaaaaaaaaaaa"
276
31715
Returns: "qqqqqrrrrrrrrrrrssssssssssstttttttttttuuuuuuuuuuuvqvvvvvvvvvvwwwwwwwwwwwxxxxxxxxxxxyyyyyyyyyyyzzzzzzzzzzzqqqqqpppppppppppooooooooooonnnnnnnnnnnmmmmmmmmmmmlllllllllllkkkkkkkkkkkjjjjjjjjjjiiiiiiiiiihhhhhhhhhhggggggggggffffffffffeeeeeeeeeeddddddddddccccccccccbbbbbbbbbbaaaaaaaaaa"
28
133
Returns: "ghijklmnfopqrstuvwxyyzzedcba"
369
39737
Returns: "jjjjkkjkkkkkkkkkkkkllllllllllllllmmmmmmmmmmmmmmnnnnnnnnnnnnnnooooooooooooooppppppppppppppqqqqqqqqqqqqqqrrrrrrrrrrrrrrssssssssssssssttttttttttttttuuuuuuuuuuuuuuvvvvvvvvvvvvvvvwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyzzzzzzzzzzzzzzzjjjjjjjjjiiiiiiiiiiiiiihhhhhhhhhhhhhhggggggggggggggffffffffffffffeeeeeeeeeeeeeeddddddddddddddccccccccccccccbbbbbbbbbbbbbbaaaaaaaaaaaaaa"
2
1
Returns: "zy"
192
4889
Returns: "eeeeeefffeffffggggggghhhhhhhiiiiiiijjjjjjjkkkkkkklllllllmmmmmmmnnnnnnnooooooopppppppqqqqqqqqrrrrrrrrssssssssttttttttuuuuuuuuvvvvvvvvwwwwwwwwxxxxxxxxyyyyyyyyzzzzzzzzdddddddcccccccbbbbbbbaaaaaaa"
131
2790
Returns: "efffffggggghhhhhiiiiijjjjjkkkkklllllmmmmmnnnnnooooopppppqqqqqrrrrrssssstttttuuuuuvvvvvwwwwwxxxxxyyyyyzzezzzzeeedddddcccccbbbbbaaaaa"
298
4889
Returns: "bbbbcccccccccccdddddddddddeeeeeeeeeeefffffffffffggggggggggghhhhhhhhhhhiiiiiiiiiibijjjjjjjjjjjkkkkkkkkkkklllllllllllmmmmmmmmmmmnnnnnnnnnnnooooooooooooppppppppppppqqqqqqqqqqqqrrrrrrrrrrrrssssssssssssttttttttttttuuuuuuuuuuuuvvvvvvvvvvvvwwwwwwwwwwwwxxxxxxxxxxxxyyyyyyyyyyyyzzzzzzzzzzzzbbbbbbaaaaaaaaaaa"
31
400
Returns: "utvvwwxxyyzzsrqponmlkjihgfedcba"
110
271
Returns: "abbbbccccddddeeeeffffgggghhhhiiiijjjjkkkkllllmmmmnnnnoooopppapqqqqrrrrssssttttuuuuuvvvvvwwwwwxxxxxyyyyyzzzzzaa"
31
362
Returns: "rsqtuvvwwxxyyzzponmlkjihgfedcba"
33
248
Returns: "jklmnopqrsttuuvvwwxxiyyzzhgfedcba"
13
55
Returns: "tuvwxsyzrqpon"
5
7
Returns: "xyzwv"
10
6
Returns: "rstuvwqxyz"
6
12
Returns: "xyzwvu"
3
3
Returns: "zyx"
1
0
Returns: "z"
3
0
Returns: "xyz"
17
35
Returns: "mnoplqrstuvwxyzkj"
7
6
Returns: "uvwxyzt"
244
18468
Returns: "kklllllllllmmmmmmmmmnnnnnnnnnooooooooopppppppppqqqqqqqqqqrrrrrrrrrrssssssssssttttttttttuuuuuuuukuuvvvvvvvvvvwwwwwwwwwwxxxxxxxxxxyyyyyyyyyyzzzzzzzzzzkkkkkkjjjjjjjjjiiiiiiiiihhhhhhhhhgggggggggfffffffffeeeeeeeeedddddddddcccccccccbbbbbbbbbaaaaaaaaa"
500
115000
Returns: "uuuuuuuuuuuvvvvvvvvvvuvvvvvvvvvvwwwwwwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyzzzzzzzzzzzzzzzzzzzzuuuuuuuutttttttttttttttttttsssssssssssssssssssrrrrrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqqpppppppppppppppppppooooooooooooooooooonnnnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmlllllllllllllllllllkkkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhgggggggggggggggggggfffffffffffffffffffeeeeeeeeeeeeeeeeeeedddddddddddddddddddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaa"
500
115696
Returns: "uuuuvvvvvvuvvvvvvvvvvvvvvwwwwwwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyzzzzzzzzzzzzzzzzzzzzuuuuuuuuuuuuuuutttttttttttttttttttsssssssssssssssssssrrrrrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqqpppppppppppppppppppooooooooooooooooooonnnnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmlllllllllllllllllllkkkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhgggggggggggggggggggfffffffffffffffffffeeeeeeeeeeeeeeeeeeedddddddddddddddddddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaa"
500
116392
Returns: "vvvvvvvvvvvvvvvvvwwwwwwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxxxxxxyyvyyyyyyyyyyyyyyyyyyzzzzzzzzzzzzzzzzzzzzvvuuuuuuuuuuuuuuuuuuuutttttttttttttttttttsssssssssssssssssssrrrrrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqqpppppppppppppppppppooooooooooooooooooonnnnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmlllllllllllllllllllkkkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhgggggggggggggggggggfffffffffffffffffffeeeeeeeeeeeeeeeeeeedddddddddddddddddddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaa"
500
117089
Returns: "vvvvvvvvwwwwwwwwwwwwwwwwwwwvwxxxxxxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyzzzzzzzzzzzzzzzzzzzzvvvvvvvvvvvuuuuuuuuuuuuuuuuuuuutttttttttttttttttttsssssssssssssssssssrrrrrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqqpppppppppppppppppppooooooooooooooooooonnnnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmlllllllllllllllllllkkkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhgggggggggggggggggggfffffffffffffffffffeeeeeeeeeeeeeeeeeeedddddddddddddddddddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaa"
500
117785
Returns: "wwwwwwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyzzzzzzzzzzzzzzzvzzzzzvvvvvvvvvvvvvvvvvvvuuuuuuuuuuuuuuuuuuuutttttttttttttttttttsssssssssssssssssssrrrrrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqqpppppppppppppppppppooooooooooooooooooonnnnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmlllllllllllllllllllkkkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhgggggggggggggggggggfffffffffffffffffffeeeeeeeeeeeeeeeeeeedddddddddddddddddddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaa"
500
118482
Returns: "wwwwwwwwxxxxxxxxxxxxxxxxxxxxyyyyyyyyyyyywyyyyyyyyzzzzzzzzzzzzzzzzzzzzwwwwwwwwwwwvvvvvvvvvvvvvvvvvvvvuuuuuuuuuuuuuuuuuuuutttttttttttttttttttsssssssssssssssssssrrrrrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqqpppppppppppppppppppooooooooooooooooooonnnnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmlllllllllllllllllllkkkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhgggggggggggggggggggfffffffffffffffffffeeeeeeeeeeeeeeeeeeedddddddddddddddddddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaa"
500
119178
Returns: "xxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyzzzzzzzzxzzzzzzzzzzzzxxxxwwwwwwwwwwwwwwwwwwwwvvvvvvvvvvvvvvvvvvvvuuuuuuuuuuuuuuuuuuuutttttttttttttttttttsssssssssssssssssssrrrrrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqqpppppppppppppppppppooooooooooooooooooonnnnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmlllllllllllllllllllkkkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhgggggggggggggggggggfffffffffffffffffffeeeeeeeeeeeeeeeeeeedddddddddddddddddddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaa"
500
119875
Returns: "yyyyyyyyyyyyyyyzzzzzyzzzzzzzzzzzzzzzyyyyxxxxxxxxxxxxxxxxxxxxwwwwwwwwwwwwwwwwwwwwvvvvvvvvvvvvvvvvvvvvuuuuuuuuuuuuuuuuuuuutttttttttttttttttttsssssssssssssssssssrrrrrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqqpppppppppppppppppppooooooooooooooooooonnnnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmlllllllllllllllllllkkkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhgggggggggggggggggggfffffffffffffffffffeeeeeeeeeeeeeeeeeeedddddddddddddddddddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaa"
500
120571
Returns: ""
500
121267
Returns: ""
500
121964
Returns: ""
500
122660
Returns: ""
500
123357
Returns: ""
500
124053
Returns: ""
500
124750
Returns: ""
500
1234
Returns: "aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbcccccccccccccccccccdddddddddddddddddddeeeeeeeeeeeeeeeeeeefffffffffffffffffffggggggggggggggggggghhhhhhhhhhhhhhhhhhhiiiiiiiiiiiiiiiiiiijjjjjjjjjjjjjjjjjjjkkkkkkkkkkkkkkkkkkklllllllllllllllllllmmmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnnnoooooooooooooooooooppppppapppppppppppppqqqqqqqqqqqqqqqqqqqrrrrrrrrrrrrrrrrrrrssssssssssssssssssstttttttttttttttttttuuuuuuuuuuuuuuuuuuuuvvvvvvvvvvvvvvvvvvvvwwwwwwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyzzzzzzzzzzzzzzzzzzzzaa"
500
110000
Returns: "ssssssssssssstttttttttttttttttttuuuuuuuuuuuuuuuuusuuuvvvvvvvvvvvvvvvvvvvvwwwwwwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyzzzzzzzzzzzzzzzzzzzzsssssrrrrrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqqpppppppppppppppppppooooooooooooooooooonnnnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmlllllllllllllllllllkkkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhgggggggggggggggggggfffffffffffffffffffeeeeeeeeeeeeeeeeeeedddddddddddddddddddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaa"
429
2453
Returns: "aaaaaaaaaabbbbbbbbbbbbbbbbccccccccccccccccddddddddddddddddeeeeeeeeeeeeeeeeffffffffffffffffgggggggggggggggghhhhhhhhhhhhhhhhiiiiiiiiiiiiiiiijjjjjjjjjjjjjjjjkkkkkkkkkkkkkkkkllllllllllllllllmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnooooooooooooooooopppppppppppppppppqqqqqqqqqqqqqqqqqrrrrrrrrrrrrrrrrrssssssssssssssssstttttttttttttttttuuuuuuuuuuuuuuuuuvvvvvvvvvvvvvvvvvwwwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxxxyyyyyyyyyayyyyyyyyzzzzzzzzzzzzzzzzzaaaaa"
28
376
Returns: "zzyyxwvutsrqponmlkjihgfedcba"
500
98754
Returns: "oppppopppppppppppppppqqqqqqqqqqqqqqqqqqqrrrrrrrrrrrrrrrrrrrssssssssssssssssssstttttttttttttttttttuuuuuuuuuuuuuuuuuuuuvvvvvvvvvvvvvvvvvvvvwwwwwwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyzzzzzzzzzzzzzzzzzzzzooooooooooooooooonnnnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmlllllllllllllllllllkkkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhgggggggggggggggggggfffffffffffffffffffeeeeeeeeeeeeeeeeeeedddddddddddddddddddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaa"
500
120000
Returns: "yyyyyyyyyzzzzzzzzzzyzzzzzzzzzzyyyyyyyyyyxxxxxxxxxxxxxxxxxxxxwwwwwwwwwwwwwwwwwwwwvvvvvvvvvvvvvvvvvvvvuuuuuuuuuuuuuuuuuuuutttttttttttttttttttsssssssssssssssssssrrrrrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqqpppppppppppppppppppooooooooooooooooooonnnnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmlllllllllllllllllllkkkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhgggggggggggggggggggfffffffffffffffffffeeeeeeeeeeeeeeeeeeedddddddddddddddddddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaa"
500
120189
Returns: "zzzzzzzzzzzzzzzzzzzyzyyyyyyyyyyyyyyyyyyyxxxxxxxxxxxxxxxxxxxxwwwwwwwwwwwwwwwwwwwwvvvvvvvvvvvvvvvvvvvvuuuuuuuuuuuuuuuuuuuutttttttttttttttttttsssssssssssssssssssrrrrrrrrrrrrrrrrrrrqqqqqqqqqqqqqqqqqqqpppppppppppppppppppooooooooooooooooooonnnnnnnnnnnnnnnnnnnmmmmmmmmmmmmmmmmmmmlllllllllllllllllllkkkkkkkkkkkkkkkkkkkjjjjjjjjjjjjjjjjjjjiiiiiiiiiiiiiiiiiiihhhhhhhhhhhhhhhhhhhgggggggggggggggggggfffffffffffffffffffeeeeeeeeeeeeeeeeeeedddddddddddddddddddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaa"
100
4806
Returns: "zzzzyyyyxxxxwwwwvvvvuuuuttttssssrrrrqqqqppppoooonnnnmmmmllllkkkkjjjjiiiihhhhggggffffeeeedddcccbbbaaa"
260
20000
Returns: "jjjkkkkkkkkkkllllllllllmmmmmmmmmmnnnnnnnnnnooooooooooppppppppppqqqqqqqqqqrrrrrrrrrrssssssssssttttttttttuuuuuuuuuuvvvvvvvvvvwwwwwwwwwwxxxxxxxxxxjyyyyyyyyyyzzzzzzzzzzjjjjjjiiiiiiiiiihhhhhhhhhhggggggggggffffffffffeeeeeeeeeeddddddddddccccccccccbbbbbbbbbbaaaaaaaaaa"