Description: 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? Input Format: 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 $$$1000$$$. Output Format: For each test case, output the minimum number of times the charges need to be used to paint all the cells of the strip. Note: 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.