Problem: You're given an array a_1, …, a_n of n non-negative integers.

Let's call it sharpened if and only if there exists an integer 1 ≤ k ≤ n such that a_1 < a_2 < … < a_k and a_k > a_{k+1} > … > 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 ≤ i ≤ 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 ≤ t ≤ 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 ≤ n ≤ 3 ⋅ 10^5).

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

It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 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.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class CodeForces extends Functions {

    private static void solve() {
      int n = sc.nextInt();
      int[] arr = sc.setintArray(n);
      out.println((helper(arr,n/2,n) || helper(arr,(n-1)/2,n))?YES:NO);
    }
    private static boolean helper(int [] arr,int half,int n){
        for(int i=0;i<=half;i++)
            if(arr[i]<i)return false;
        for(int i=n-1;i>=half;i--)
            if(arr[i]<(n-1)-i)return false;
        return true;
    }


    public static void main(String[] args) {
        int testCase = 1;
        testCase= sc.nextInt();
        while (testCase-->0) solve();
        sc.close();
        out.flush();
        out.close();
    }

    static Scanner sc = new Scanner(); // Input
//    static  PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));  // Fast output
    static PrintStream out = new PrintStream(System.out);   // output
}


class Functions {
    public static int mod = (int)1e9+7;
    public static final int INT_MAX = Integer.MAX_VALUE;
    public static final int INT_MIN = Integer.MIN_VALUE;
    public static final long LONG_MAX = Long.MAX_VALUE;
    public static final long LONG_MIN = Long.MIN_VALUE;
    public static final double DOUBLE_MAX = Double.MAX_VALUE;
    public static final double DOUBLE_MIN = Double.MIN_VALUE;
    public static final String YES = "YES";
    public static final String NO = "NO";

    public static void sort(int[] a,boolean isAscending){
        ArrayList<Integer> temp = new ArrayList<>();
        for (int j : a) temp.add(j);
        sort(temp,isAscending);
        for(int i=0;i<a.length;i++)a[i] = temp.get(i);
    }

    public static void sort(List list,boolean isAscending){
        if(isAscending)
            Collections.sort(list);
        else Collections.sort(list,Collections.reverseOrder());
    }
    // euclidean algorithm
    public static long gcd(long a, long b) {
        // time O(max (loga ,logb))
        long x = Math.min(a,b);
        long y = Math.max(a,b);
        if (y % x == 0) return x;
        return gcd(y%x,x);
    }
    public static long lcm(long a, long b) {
        // lcm(a,b) * gcd(a,b) = a * b
        return (a / gcd(a, b)) * b;
    }

    public static long factorial(long n){
        long fact = 1L;
        for(int i=2;i<=n;i++)fact = (fact*i)%mod;
        return fact;
    }
    public static long firstDivisor(long n){
        if(n==1)return n;
        for(long i=2;i*i<=n;i++)
            if(n%i==0)return i;
        return -1;
    }
    public static long power(long x,long n){
        // calculate x^n %mod using binary exponentiation
        // time : O(logn)
        long ans = 1;
        while(n>0){
            if(n%2!=0){
                ans *= x;
                n--;
            }else {
                x *= x;
                n/=2;
            }
            x %=mod;
            ans %=mod;
        }
        return ans;
    }
    public  static int ncr(int n, int r){
        // time O(n+r)
        if (r > n)
            return 0;
        long[] inv = new long[r + 1];
        inv[1] = 1;
        // Getting the modular inversion
        // for all the numbers
        // from 2 to r with respect to m
        for (int i = 2; i <= r; i++) {
            inv[i] = mod - (mod / i) * inv[(int) (mod % i)] % mod;
        }
        int ans = 1;
        // for 1/(r!) part
        for (int i = 2; i <= r; i++) {
            ans = (int) (((ans % mod) * (inv[i] % mod)) % mod);
        }
        // for (n)*(n-1)*(n-2)*...*(n-r+1) part
        for (int i = n; i >= (n - r + 1); i--) {
            ans = (int) (((ans % mod) * (i % mod)) % mod);
        }
        return ans;
    }
    public static void reverseArray(int[] a){
        int left = 0;
        int right = a.length-1;
        while (left<right){
            int temp =a[left];
            a[left] = a[right];
            a[right] = temp;
            left++;
            right--;
        }
    }
}

class Scanner {
    private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private StringTokenizer st = new StringTokenizer("");
    public String next(){
        while (!st.hasMoreTokens())
            try {
                st = new StringTokenizer(br.readLine());
            }catch (IOException e){
                e.printStackTrace();
            }
        return st.nextToken();

    }
    public int nextInt(){return Integer.parseInt(next());}
    public long nextLong(){return Long.parseLong(next());}
    public double nextDouble(){return Double.parseDouble(next());}
    public int[] setintArray(int n){
        int[] arr =new int[n];
        for(int i=0;i<n;i++)arr[i] = nextInt();
        return arr;
    }
    public long[] setlongArray(int n){
        long[] arr =new long[n];
        for(int i=0;i<n;i++)arr[i] = nextLong();
        return arr;
    }
    public int[][] set2DintArray(int row, int col){
        int[][] arr = new int[row][col];
        for(int i=0;i<row;i++)
            for(int j= 0;j<col;j++)
                arr[i][j] = nextInt();
        return arr;
    }
    public long[][] set2DlongArray(int row, int col){
        long[][] arr = new long[row][col];
        for(int i=0;i<row;i++)
            for(int j= 0;j<col;j++)
                arr[i][j] = nextLong();
        return arr;
    }
    public void close(){
        try{
            br.close();
        }catch (IOException e){
            e.printStackTrace();
        }
    }
}