CF1927G.Paint Charges

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题目描述

A horizontal grid strip of $n$ cells is given. In the $i$ -th cell, there is a paint charge of size $a_i$ . This charge can be:

either used to the left — then all cells to the left at a distance less than $a_i$ (from $\max(i - a_i + 1, 1)$ to $i$ inclusive) will be painted,
or used to the right — then all cells to the right at a distance less than $a_i$ (from $i$ to $\min(i + a_i - 1, n)$ inclusive) will be painted,
or not used at all.

Note that a charge can be used no more than once (that is, it cannot be used simultaneously to the left and to the right). It is allowed for a cell to be painted more than once.

What is the minimum number of times a charge needs to be used to paint all the cells of the strip?

输入格式

The first line of the input contains an integer $t$ ( $1 \le t \le 100$ ) — the number of test cases in the test. This is followed by descriptions of $t$ test cases.

Each test case is specified by two lines. The first one contains an integer $n$ ( $1 \le n \le 100$ ) — the number of cells in the strip. The second line contains $n$ positive integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le n$ ), where $a_i$ is the size of the paint charge in the $i$ -th cell from the left of the strip.

It is guaranteed that the sum of the values of $n$ in the test does not exceed $1000$ .

输出格式

For each test case, output the minimum number of times the charges need to be used to paint all the cells of the strip.

输入输出样例

输入#1

13
1
1
2
1 1
2
2 1
2
1 2
2
2 2
3
1 1 1
3
3 1 2
3
1 3 1
7
1 2 3 1 2 4 2
7
2 1 1 1 2 3 1
10
2 2 5 1 6 1 8 2 8 2
6
2 1 2 1 1 2
6
1 1 4 1 3 2

输出#1

说明/提示

In the third test case of the example, it is sufficient to use the charge from the $1$ -st cell to the right, then it will cover both cells $1$ and $2$ .

In the ninth test case of the example, you need to:

use the charge from the $3$ -rd cell to the left, covering cells from the $1$ -st to the $3$ -rd;
use the charge from the $5$ -th cell to the left, covering cells from the $4$ -th to the $5$ -th;
use the charge from the $7$ -th cell to the left, covering cells from the $6$ -th to the $7$ -th.

In the eleventh test case of the example, you need to:

use the charge from the $5$ -th cell to the right, covering cells from the $5$ -th to the $10$ -th;
use the charge from the $7$ -th cell to the left, covering cells from the $1$ -st to the $7$ -th.

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