JNEXT - Just Next !!!

DevG likes too much fun to do with numbers. Once his friend Arya came and gave him a challenge, he gave DevG an array of digits which is forming a number currently (will be called as given number). DevG was challanged to find the just next greater number which can be formed using digits of given number. Now DevG needs your help to find that just next greater number and win the challenge.

Input

The first line have t number of test cases (1 <= t <= 100). In next 2*t lines for each test case first there is number n (1 <= n <= 1000000) which denotes the number of digits in given number and next line contains n digits of given number separated by space.

Output

Print the just next greater number if possible else print -1 in one line for each test case.

Note : There will be no test case which contains zero in starting digits of any given number.

Example

Input:
2
5
1 5 4 8 3
10
1 4 7 4 5 8 4 1 2 6

Output:
15834
1474584162

Added by:! include(L.ppt)
Date:2012-08-31
Time limit:1.297s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:MNNIT OPC 31-08-2012

hide comments
2019-03-20 19:52:22
Quite easy ,
NlogN in worst case would work fine
used multiset and upper_bounds.....
matter of seconds
2019-01-30 14:02:19
Done using next_permution function in c++ STL.. LOL
2018-12-06 12:44:59
How to do it with stacks?
2018-11-17 09:24:47
AC in one go!! Yay!
2018-10-31 14:09:43
Alright! Done using sorting! Previous O(NlogN) solution using multiset gave TLE but stl sort works! Guess STL sort has slightly better than NlogN runtime..
2018-10-30 15:10:43
10^6 is too big dataset for my beautiful nlogn solution using multiset and binarysearch.. :(
2018-10-24 11:15:22
Little hard,
try doing it for test cases like - 1 6 8 7 5
and consider the failing test cases(-1) too like 741 or 4
2018-10-09 17:40:09
I am running this code in another IDE and getting this correct in JAVA but getting Wrong Answer here .Can Somebody tell me corner cases that I need to cover
2018-09-30 17:39:57
Easy AC in one go. Check for this test case
1 0 8 7 6
2018-09-21 20:26:21
Took 20 attempt to get it correct :( for 25th

Last edit: 2018-09-25 17:41:47
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