Find a Subsequence

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Given an array A of N integers A[0], A[1], ..., A[N-1] and a string B which is a permutation of "12345".
You have to find a subsequence of 5 elements from A having distinct values such that their relative order is same as B.
Meaning that, if (i₀, i₁, i₂, i₃, i₄) are the indexes of such a subsequence (0 <= i₀ < i₁ < i₂ < i₃ < i₄ < N) then:

A[i₀] is the B[0]-th smallest element among the 5 numbers.

A[i₁] is the B[1]-th smallest element among the 5 numbers.

A[i₂] is the B[2]-th smallest element among the 5 numbers.

A[i₃] is the B[3]-th smallest element among the 5 numbers.

A[i₄] is the B[4]-th smallest element among the 5 numbers.

Input

The first line of input contains T(<=60) which is the number of tests cases. The first line of each test case will be an integer N (5<=N<=1000) and a string B containing a permutation of "12345". Next line will contain N integers A[0], A[1], ..., A[N-1]. Each of them will be between -10⁹ and +10⁹ (inclusive).

Output

For each test case output five space separated integers in ascending order which are the indexes (i₀, i₁, i₂, i₃, i₄) of a five length subsequence described before. You may output any solution. If there is no solution just output "-1" without quotes.

Example

Input:
2
7 32145
6 17 5 3 13 8 10
7 12345
10 20 30 40 40 20 10

Output:
0 2 3 5 6
-1

Explanation of 1st sample: {0, 2, 3, 5, 6} is a valid solution because the values of those indexes {6, 5, 3, 8, 10} will have ranks {3, 2, 1, 4, 5} after sorting. But {0, 2, 3, 4, 5} is not a solution as the values {6, 5, 3, 13, 8} will have ranks {3, 2, 1, 5, 4} after sorting.
Explanation of 2nd sample: There is no five length subsequence in the array that will have ranks {1, 2, 3, 4, 5} after sorting.

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Date:	2011-12-07
Time limit:	9s-14s
Source limit:	50000B
Languages:	All