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.

Starter code:

Solutions:
for _ in range(int(input())):
    n=int(input())
    li=list(map(int,input().split()))
    ans=0
    for i in range(n):
        if li[i]>=i:
            ans+=1
        else:
            break
    for i in range(n):
        if li[n-1-i]>=i:
            ans+=1
        else:
            break
    if ans>n:
        print("Yes")
    else:
        print("No")

for nt in range(int(input())):
	n=int(input())
	l=list(map(int,input().split()))
	point = -1
	for i in range(n):
		if l[i]<i:
			point = i-1
			break
	if point == -1:
		print ("Yes")
	else:
		flag=0
		for i in range(n-1,point-1,-1):
			if l[i]<(n-1-i):
				flag=1
				print ("No")
				break
		if flag==0:
			print ("Yes")

t = int(input().rstrip())

for i in range(t):
    n = int(input().rstrip())
    nums = list(map(int, input().rstrip().split()))
    forw = 0
    back = n-1

    for j in range(n):
        if nums[j] >= j:
            forw = j
        else:
            break
    
    for j in range(1, n+1):
        if nums[-j] >= j-1:
            back = n-j
        else:
            break
    
    if forw >= back:
        print("Yes")
    else:
        print("No")

def f(a):
    for i in range(len(a)):
        if a[i] < i: return i-1
    return len(a)-1

def solve(a):
    i = f(a)
    j = len(a) - 1 - f(a[::-1])
    return "Yes" if i >= j else "No"


n = int(input())
for i in range(n):
    input()
    a = list(map(int, input().strip().split()))
    print(solve(a))

import sys
input = sys.stdin.readline

t = int(input())

for testcase in range(t):
    n = int(input())
    a = list(map(int,input().split()))

    left = n-1
    for i in range(n):
        if a[i] <= i-1:
            left = i-1
            break
    
    right = 0
    for i in range(n-1,-1,-1):
        if a[i] < n-1-i:
            right = i+1
            break
    

    if right <= left:
        print('Yes')
    else:
        print('No')

T = int(input())
for _ in range(T):
    N = int(input())
    A = list(map(int,input().split()))
    if N%2:
        X = [i if i<N//2 else N-i-1 for i in range(N)]
        if all(a>=x for a,x in zip(A,X)):
            print('Yes')
        else:
            print('No')
    else:
        X = [i if i<N//2+1 else N-i-1 for i in range(N)]
        if all(a>=x for a,x in zip(A,X)):
            print('Yes')
            continue
        X[N//2-1], X[N//2] = X[N//2], X[N//2-1]
        if all(a>=x for a,x in zip(A,X)):
            print('Yes')
        else:
            print('No')