You're given an array $a_1, \ldots, a_n$ of $n$ non-negative integers.

Let's call it sharpened if and only if there exists an integer $1 \le k \le n$ such that $a_1 < a_2 < \ldots < a_k$ and $a_k > a_{k+1} > \ldots > a_n$. In particular, any strictly increasing or strictly decreasing array is sharpened. For example:  The arrays $[4]$, $[0, 1]$, $[12, 10, 8]$ and $[3, 11, 15, 9, 7, 4]$ are sharpened;  The arrays $[2, 8, 2, 8, 6, 5]$, $[0, 1, 1, 0]$ and $[2, 5, 6, 9, 8, 8]$ are not sharpened. 

You can do the following operation as many times as you want: choose any strictly positive element of the array, and decrease it by one. Formally, you can choose any $i$ ($1 \le i \le n$) such that $a_i>0$ and assign $a_i := a_i - 1$.

Tell if it's possible to make the given array sharpened using some number (possibly zero) of these operations.


-----Input-----

The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 15\ 000$)  — the number of test cases. The description of the test cases follows.

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

The second line of each test case contains a sequence of $n$ non-negative integers $a_1, \ldots, a_n$ ($0 \le a_i \le 10^9$).

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


-----Output-----

For each test case, output a single line containing "Yes" (without quotes) if it's possible to make the given array sharpened using the described operations, or "No" (without quotes) otherwise.


-----Example-----
Input
10
1
248618
3
12 10 8
6
100 11 15 9 7 8
4
0 1 1 0
2
0 0
2
0 1
2
1 0
2
1 1
3
0 1 0
3
1 0 1

Output
Yes
Yes
Yes
No
No
Yes
Yes
Yes
Yes
No



-----Note-----

In the first and the second test case of the first test, the given array is already sharpened.

In the third test case of the first test, we can transform the array into $[3, 11, 15, 9, 7, 4]$ (decrease the first element $97$ times and decrease the last element $4$ times). It is sharpened because $3 < 11 < 15$ and $15 > 9 > 7 > 4$.

In the fourth test case of the first test, it's impossible to make the given array sharpened.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 't = int(input().rstrip())\n\nfor i in range(t):\n    n = int(input().rstrip())\n    nums = list(map(int, input().rstrip().split()))\n    forw = 0\n    back = n-1\n\n    for j in range(n):\n        if nums[j] >= j:\n            forw = j\n        else:\n            break\n    \n    for j in range(1, n+1):\n        if nums[-j] >= j-1:\n            back = n-j\n        else:\n            break\n    \n    if forw >= back:\n        print("Yes")\n    else:\n        print("No")'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13255