### Problem Statement

A classic string hashing algorithm can be simply described by the following code, where long is a signed 64-bit integer type:
long hash(str){
long hash = 5381;

for(i = 0; i<str.length; i++)
hash = (hash * 33) ^ str[i]; // '^' denotes XOR

return hash;
}

You are given a long[] hashes. Each element of hashes is a result of applying the described hashing algorithm to a randomly generated string.

Your task is to invert this algorithm. You must return a String[] which should contain the same number of elements as hashes. Applying the described hashing algorithm to each element of your return should produce the corresponding element of hashes. Each element of your return should contain at most 10,000 characters, and each character of each element of your return must have ASCII code between 33 and 126, inclusive. If you cannot find a string which hashes to a certain element of hashes, set the corresponding element of your return to "".

Your score for a test case will be the sum of 1/(length of returned string) over all correct elements of your return of non-zero length. Invalid return of any kind, including having the wrong number of elements in your return or characters with ASCII codes less than 33 or greater 126 results in zero score for that test case. Zero-length strings in your return simply don't contribute to your score. Valid strings that don't hash to the correct value will be treated in the same way as empty strings. Your overall score will be the sum of scores for individual test cases.

The input will be generated in a following way:
1. the number of strings will be chosen between 10 and 1000, inclusive
2. the length of each string will be chosen independently between 4 and 20, inclusive
3. each character of each string will be chosen between 33 and 126, inclusive
All variables are chosen randomly and uniformly.

### Definition

 Class: InverseHash Method: inverse Parameters: long[] Returns: String[] Method signature: String[] inverse(long[] hashes) (be sure your method is public)

### Notes

-There are 100 provisional test cases.

### Constraints

-The time limit is 10 seconds.
-The memory limit is 1024MB.

### Examples

0)

 "1"
Returns:
"920 hashes
0: -6O&amp;Qk9~czXENxRw! hashes to -4459230493565586372
1: LRi~~&amp;ZA!GrUU{V hashes to 5501830964056691222
2: dtzY&lt;EUr-\\(43~^ hashes to -8337223747280775818
3: RU~nLF6Qnu hashes to 8245112492441997732
4: *Wm- hashes to 6380591320
5: L929U}MRV#}-A0tY hashes to 1460305034284426165
6: &gt;`YjL}HrF&lt;Zm%0,I hashes to 2572936786439756830
7: s)`PqJ3Z4pG\\xm^UG hashes to -5525835650212379589
8: &lt;Rk%H}D&gt;PJ5!~={0 hashes to 3928777983488211852
9: `r*0*(DYq3!_wW&gt;KJ6 hashes to 6271036284597753639
...
"
1)

 "2"
Returns:
"911 hashes
0: &lt;l-Jk)-}lr-D hashes to -9215950419413139433
1: /Ood6 hashes to 210553093784
2: J``Hc)=h hashes to 7571000880659480
3: Sgoo5 hashes to 210684487780
4: GEURYiJzlMo hashes to -4637535168201879794
5: .V;\$uM5' hashes to 7566717596914600
6: x3zHC'6{Z+f5 hashes to -5887852083349028841
7: n2PC6O2kny5DMO hashes to 3477693585084717134
8: ?&gt;]s%E-s hashes to 7567427147094292
9: ,l{V&lt;87Jb?!J hashes to 8420151027292092103
...
"
2)

 "3"
Returns:
"942 hashes
0: AISo-\\ hashes to 6951787708576
1: TYE=]' hashes to 6952426506826
2: qN/#*Y9k@pEz; hashes to -7062776074989436637
3: rT_&amp; hashes to 6383284410
4: &lt;H.,YK^j3UU= hashes to -9169455319257574853
5: m8o=9% hashes to 6950803341374
6: 6r@KDMD{`0I&gt;3% hashes to 8549194571211681485
7: &amp;~o?zLrs%_;`{^ hashes to -7747257036548627714
8: hui:v_DM%nwHhy;fZ hashes to 2733304970611327977
9: DEy*k#|;!VH?* hashes to 2438409207087451346
...
"
3)

 "4"
Returns:
"761 hashes
0: z};Gz= hashes to 6951664462105
1: CKSr&lt;&gt;^=]U=&lt;@M)H24 hashes to -2775172367091542514
2: P4jkv}lpqD hashes to 8245155484588884834
3: jgr~~w9EIjS hashes to -4668623916380232063
4: -9r%l?aP\$4)7kyh hashes to -7156532954763063600
5: G12dr5XGFQojn(6w\$&amp;2 hashes to 8199977158657504856
6: ;59]('D\"WK)^_ hashes to -1286846458925831662
7: e5{_\$k hashes to 6950511923134
8: y4@fJe~F hashes to 7570241829036505
9: -(M*nay hashes to 229293420697617
...
"
4)

 "5"
Returns:
"852 hashes
0: 4~]\\`Umg%xY7{T}A\\=oi hashes to -2802808815202892714
1: _x&lt;6vb(_C=XE hashes to -4339844057738111384
2: .3{\"]y=D,Rj hashes to -4774862133067818200
3: L.UvrP(\\.py-/ hashes to -4407161853640047305
4: ^Z.15n0 hashes to 229437363778869
5: SrSNUvHbL2 hashes to 8245203538883335086
6: ~gY% hashes to 6383414528
7: I1:Hu9_ hashes to 229420887377276
8: EJk5jt hashes to 6951630305610
...
"
5)

 "6"
Returns:
"586 hashes
0: KhFZo[eo+h9`2,h+T0. hashes to 1402066366173238857
1: nu(i)mS hashes to 229380938641288
2: t8HID&gt;po)cv hashes to -4668656540645664303
3: p%86Ju3'p hashes to 249806158964331205
4: fF9y&lt;up\$6&amp;b hashes to -4684997711342640790
5: \"z^&gt;XVJr_f:W[rjwI8 hashes to -6212120274168065990
6: G9\$bufxQ=/0\$8 hashes to 334084547605398201
7: C\$hK hashes to 6383736737
8: =E&amp;7mB^Sri[Tw6s&amp;vVCZ hashes to -4345540928270390793
9: JZiGFhFjr`CoP4G hashes to 7000553712153281476
...
"
6)

 "7"
Returns:
"506 hashes
0: 27?VU!7/i4:`fj.|a hashes to 334865303041701053
1: &gt;&lt;gk.cpo&amp;qei5GmNZ=# hashes to -1747577732427159657
2: HSJb/?CF.wMwMF7 hashes to -6499770471338768420
3: #;K^'Z hashes to 6948243273749
4: ;G\"w(1m:\$BM hashes to -4748056293055541175
5: =DKZ@,@ hashes to 229315629223393
6: |\"z-pR\$+*] hashes to 8243797952660047446
7: |4sw7RRDz^5 hashes to -4656599248226620757
8: EPT^?yy.g%G@|&amp;JjE? hashes to 8767638268308946894
9: X'!el&lt;*9{irNvtAw5W,R hashes to -2089566484131462597
...
"
7)

 "8"
Returns:
"289 hashes
0: \"c`~q';hq)A hashes to -4784496259766143610
1: 2@+LD7uy^5*&amp; hashes to 8992037327646049288
2: *%\$\"/mE]a:; hashes to -4769448707389501642
3: 9kA[iVC hashes to 229321700083345
4: kH7XQ&gt;3&gt;eRZ^XClI8 hashes to -6500336944718404546
5: 2`=7{*B\$E&amp; hashes to 8240639889548478185
6: SlTN9^8WW hashes to 249855720111276927
7: ]U+;lRab6 hashes to 249853765054500342
8: [yODOLe7C+Ewn&amp;IShA hashes to -8510154841288666308
9: _ze\$_O&amp;hns:aZA`R!GD hashes to 9125600201344499442
...
"
8)

 "9"
Returns:
"164 hashes
0: &gt;uXM&gt;AMU9JVqI(; hashes to -5554446056225879374
1: dmo]2) hashes to 6950387215557
2: =&lt;V?ca*(^ hashes to 249722525005326227
3: A!l\"La2'hY@ hashes to -4639165987492321534
4: m?F}I*-PV hashes to 249791335504227908
5: ~/o'dX@]jtPe6 hashes to 5689051823629226240
6: -L~)V[.,M)nD/En hashes to 6775712747933239126
7: IuG}wfw43*P]M^ hashes to -3181329448533517418
8: 9xj&lt;XEQ6%J98fsW5)V hashes to -2442187885070038962
9: XbP\\-&amp;jjKcI|u{hS\" hashes to -1386612256954665102
...
"
9)

 "10"
Returns:
"620 hashes
0: gXTcy hashes to 210625163764
1: L%CE~qhG hashes to 7570830569724010
2: |mOF&lt;r hashes to 6951307027123
3: }e\$FU9GT{s hashes to 8243756817752295560
4: FG7xk, hashes to 6951742605964
5: Z.~A]j!7,~D\$6R0m~%^ hashes to -5459307163877088575
6: D*&gt;m[^u~)'?y)naL%E hashes to 8416537084852756884
7: -tx&amp;)cuPp54,kl?^1W hashes to -9181173968239343760
8: Auc8djCa(0L%dc&gt;\"p.Z hashes to 1569005996737215432
9: ?./(i hashes to 210575410330
...
"

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10679

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14162&pm=10679

Unknown

#### Problem categories:

Encryption/Compression