Era

题意翻译

### 题目描述 给一个长度为 $n$ 的序列 $a_1,a_2,\dots,a_n$，每次可以往序列中插入任意个整数，求最少插入多少个整数时 $\forall i,a_i\le i$。 ### 输入格式 第一行输入一个正整数 $t$ 表示数据组数。 每组数据输入两行，第一行为一个正整数 $n$ 表示一个序列，第二行 $n$ 个正整数表示序列 $a$。 ### 输出格式 对于每组数据输出一行一个整数表示答案。 ### 数据范围 $1\le t\le200,1\le n\le100,1\le a_i\le10^9$。

题目描述

Shohag has an integer sequence $ a_1, a_2, \ldots, a_n $ . 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] $ and he selects $ k = 2 $ , then after the operation he can obtain one of the sequences $ [\underline{2},3,3,4] $ , $ [3,\underline{2},3,4] $ , $ [3,3,\underline{2},4] $ , or $ [3,3,4,\underline{2}] $ . Shohag wants this sequence to satisfy the following condition: for each $ 1 \le i \le |a| $ , $ a_i \le i $ . 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.

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 200 $ ) — the number of test cases. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 100 $ ) — the initial length of the sequence. The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le 10^9 $ ) — the elements of the sequence.

输出格式

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

输入输出样例

输入样例 #1

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

输出样例 #1

1
3
0
696966

说明

In the first test case, we have to perform at least one operation, as $ a_2=3>2 $ . We can perform the operation $ [1, 3, 4] \rightarrow [1, \underline{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] \rightarrow [1, 2, \underline{3}, 5, 7, 4] \rightarrow [1, 2, 3, \underline{4}, 5, 7, 4] \rightarrow [1, 2, 3, 4, 5, \underline{3}, 7, 4] $ . In the third test case, the sequence already satisfies the condition.