???题目2 : Reverse Suffix Array

描述

There is a strong data structure called "Suffix Array" which can effectively solve string problems.

Let S=s1s2...sn be a string and let S[i,j] denote the substring of S ranging from i to j. The suffix array A of S is now defined to be an array of integers providing the starting positions of suffixes of S in lexicographical order. This means, an entry A[i] is the starting position of the i-th smallest suffix in S and thus for all 1 < i ≤ n:  S[A[i-1], n] < S[A[i], n].

For example: the suffix array of “banana” is [6, 4, 2, 1, 5, 3].

Here comes another problem called "Reverse Suffix Array".

Given a suffix array, you need to figure out how many lower case strings are there whose suffix array is the same as the given suffix array.

输入

First line contains a positive number T which means the number of test cases.

For each test cases, first line contains a positive number N, the second line contains N integer(s) which indicates the suffix array A.

1 ≤ T ≤ 10, 1 ≤ N ≤ 100,000

1 ≤ A[i] ≤ N (i = 1...N)

输出

For each test case, output one line contains the answer. If no qualified string exists, output 0.