## Algorithm

A. Era
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Shohag has an integer sequence a1,a2,,an�1,�2,…,��. He can perform the following operation any number of times (possibly, zero):

• Select any positive integer k (it can be different in different operations).
• Choose any position in the sequence (possibly the beginning or end of the sequence, or in between any two elements) and insert k into the sequence at this position.
• This way, the sequence a changes, and the next operation is performed on this changed sequence.

For example, if a=[3,3,4]�=[3,3,4] and he selects k=2�=2, then after the operation he can obtain one of the sequences [2,3,3,4][2_,3,3,4][3,2,3,4][3,2_,3,4][3,3,2,4][3,3,2_,4], or [3,3,4,2][3,3,4,2_].

Shohag wants this sequence to satisfy the following condition: for each 1i|a|1≤�≤|�|aii��≤�. Here, |a||�| denotes the size of a.

Help him to find the minimum number of operations that he has to perform to achieve this goal. We can show that under the constraints of the problem it's always possible to achieve this goal in a finite number of operations.

Input

The first line contains a single integer t (1t2001≤�≤200)  — the number of test cases.

The first line of each test case contains a single integer n (1n1001≤�≤100) — the initial length of the sequence.

The second line of each test case contains n integers a1,a2,,an�1,�2,…,�� (1ai1091≤��≤109) — the elements of the sequence.

Output

For each test case, print a single integer  — the minimum number of operations needed to perform to achieve the goal mentioned in the statement.

Example
input
Copy
4
3
1 3 4
5
1 2 5 7 4
1
1
3
69 6969 696969

output
Copy
1
3
0
696966

Note

In the first test case, we have to perform at least one operation, as a2=3>2�2=3>2. We can perform the operation [1,3,4][1,2,3,4][1,3,4]→[1,2_,3,4] (the newly inserted element is underlined), now the condition is satisfied.

In the second test case, Shohag can perform the following operations:

[1,2,5,7,4][1,2,3,5,7,4][1,2,3,4,5,7,4][1,2,3,4,5,3,7,4][1,2,5,7,4]→[1,2,3_,5,7,4]→[1,2,3,4_,5,7,4]→[1,2,3,4,5,3_,7,4].

In the third test case, the sequence already satisfies the condition.

## Code Examples

### #1 Code Example with C++ Programming

Code - C++ Programming

#include&llt;bits/stdc++.h>
using namespace std;

#define ll long long
#define endl '\n'
#define debug(n) cout&llt;&llt;(n)&llt;&llt;endl;
const ll INF = 2e18 + 99;

int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);

int t;
cin>>t;
while(t--){
int n;
cin>>n;
int maxel = 0;
int x;
for(int i = 1; i &llt;= n; i++){
cin>>x;
if(x - i > maxel){
maxel = x - i;
}
}
cout&llt;&llt;maxel&llt;&llt;endl;
}

}
Copy The Code &

Input

cmd
4
3
1 3 4
5
1 2 5 7 4
1
1
3
69 6969 696969

Output

cmd
1
3
0
696966