J. Know Your Place
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array $$$a$$$ of $$$n$$$ positive integers.

You may perform the following operation any number of times:

  • Choose an index $$$i$$$ ($$$1 \le i \le |a|$$$) such that $$$a_i \le i$$$, where $$$|a|$$$ denotes the current length of the array, and delete the element $$$a_i$$$ from the array; after the deletion, all elements to the right of position $$$i$$$ shift one position to the left.

Determine whether it is possible to delete all elements of the array using these operations.

Input

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

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 3 \cdot 10^5$$$) — the length of the array.

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 array.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$3 \cdot 10^5$$$.

Output

For each test case, print YES if it is possible to delete all elements of the array, and NO otherwise.

Example
Input
2
3
1 2 1
4
7 1 2 4
Output
YES
NO
Note

In the first test case,

  • Select $$$i = 2$$$ as $$$a_2 \le 2$$$, delete $$$a_2$$$, the array becomes $$$[1, 1]$$$;
  • Select $$$i = 2$$$ as $$$a_2 \le 2$$$, delete $$$a_2$$$, the array becomes $$$[1]$$$;
  • Select $$$i = 1$$$ as $$$a_1 \le 1$$$, delete $$$a_1$$$, the array becomes empty.