[Solution] Positive array CodeChef Solution

A 1-indexed array is called positive if every element of the array is greater than or equal to the index on which it lies. Formally, an array B$B$ of size M$M$ is called positive if Bi≥i$B_i\ge i$ for each 1≤i≤M$1\le i\le M$.

For example, the arrays [1],[2,2],[3,2,4,4]$[1],[2,2],[3,2,4,4]$ are positive while the arrays [2,1],[3,1,2]$[2,1],[3,1,2]$ are not positive.

You are given an array A$A$ containing N$N$ integers. You want to distribute all elements of the array into some positive arrays. The elements of a positive array might not occur in the order they appear in the array A$A$.

Find the minimum number of positive arrays that the elements of the array A$A$ can be divided into.

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Please see the sample cases below for more clarity.

Input Format

• The first line of input will contain a single integer T$T$, denoting the number of test cases.

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• Each test case consists of two lines of input.
  • The first line of each test case contains an integer N$N$ — the number of elements in the array A$A$.
  • The next line contains N$N$ space-separated integers A1,A2,…,AN$A_1,A_2,\dots ,A_N$ — the elements of array A$A$.

Output Format

For each test case, output on a new line the minimum number of positive arrays that the elements of the array A$A$ can be divided into.​

Constraints

• 1≤T≤104$1\le T\le {10}^4$
• 1≤N≤105$1\le N\le {10}^5$
• 1≤Ai≤N$1\le A_i\le N$
• The sum of N$N$ over all test cases won't exceed 2⋅105