There are $$$n$$$ flowers in a row, the $$$i$$$-th of them initially has a positive height of $$$h_i$$$ meters.

Every second, the wind will blow from the left, causing the height of some flowers to decrease.

Specifically, every second, for each $$$i$$$ from $$$1$$$ to $$$n$$$, in this order, the following happens:

If $$$i = n$$$ or $$$h_i \gt h_{i + 1}$$$, the value of $$$h_i$$$ changes to $$$\max(0, h_i - 1)$$$.

How many seconds will pass before $$$h_i=0$$$ for all $$$1 \le i \le n$$$ for the first time?

Input

Each test contains multiple test cases. The first line of input contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the number of flowers.

The second line of each test case contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le 10 ^ 9$$$) — the heights of the flowers.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case, output a single integer — the number of seconds that will pass before $$$h_i=0$$$ for all $$$1 \le i \le n$$$.

Note

In the first test case, the flower heights change as follows: $$$[1, 1, 2] \rightarrow [1, 1, 1] \rightarrow [1, 1, 0] \rightarrow [1, 0, 0] \rightarrow [0, 0, 0]$$$.

In the second test case, the flower heights change as follows: $$$[3, 1] \rightarrow [2, 0] \rightarrow [1, 0] \rightarrow [0, 0]$$$.

Basil's Garden

Examples