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.math.*;
import java.util.*;

public class Task {
  private static final int IO_BUFFERS = 1024 * 1024;
  private static final long MODULO = (long) Math.pow(10, 9) + 7;
  private static final long LIMIT = Long.MAX_VALUE>>2;
  private static FastReader reader = new FastReader();
  private static FastWriter writer = new FastWriter();

  static class Solution {
    int N;
    int[] A;

    void readInput() throws IOException {
      N = reader.nextInt();
      A = reader.fillIntegerArray(N);
    }

   String solve() {
      int pivot = -1;
      for(int i = 0; i < N; i++) {
        if (pivot == -1) {
          if (A[i] >= i) {
            continue;
          } else {
            pivot = i;
            if (A[i] < N-1 - i) return "No";
          }
        } else {
          if (A[i] < N - 1 - i) return "No";
        }
      }

      if (N%2 == 0 && pivot == N/2 && A[pivot-1] == A[pivot] && A[pivot-1]==A[pivot]) return "No";

      return "Yes";
   }

    public Solution() throws IOException {
      readInput();
      writer.println(solve());
    }
  }

  public static void main(String[] args) {
    long startTime = System.currentTimeMillis();
    try {
      int T = reader.nextInt();
      for (int t = 0; t < T; t++) new Solution();
      writer.close();
    } catch (IOException e) {
      throw new RuntimeException(e);
    }
    System.err.println("\ntime: " + (System.currentTimeMillis() - startTime) + "ms");
  }


  static class HMultiset<T> extends HashMap<T, Integer> {
    void add(T key) {
      Integer count = get(key);
      put(key, count == null ? 1 : count + 1);
    }

    @SuppressWarnings(value = "unchecked")
    @Override
    public Integer remove(Object key) {
      if (!containsKey(key)) return null;

      int count = get(key);
      if (count > 1) return put((T) key, count - 1);

      return super.remove(key);
    }
  }
  static class FastWriter{private final StringBuilder out;public FastWriter(){out=new StringBuilder(IO_BUFFERS);}    public FastWriter print(Object object){out.append(object);return this;}    public FastWriter print(String format,Object...args){out.append(String.format(format,args));return this;}    public FastWriter println(Object object){out.append(object).append("\n");return this;}    public void close()throws IOException{System.out.print(out);}}
  static class FastReader{private DataInputStream din;private byte[]buffer;private int bufferPointer,bytesRead;public FastReader(){din=new DataInputStream(System.in);buffer=new byte[IO_BUFFERS];bufferPointer=bytesRead=0;}    public FastReader(String file_name)throws IOException{din=new DataInputStream(new FileInputStream(file_name));buffer=new byte[IO_BUFFERS];bufferPointer=bytesRead=0;}    public String readLine()throws IOException{StringBuilder sb=new StringBuilder();int c;while((c=read())!=-1){if(c=='\n'){if(sb.length()>0)break;else continue;}        sb.append((char)c);}        return sb.toString();}    public int nextInt()throws IOException{int ret=0;byte c=read();while(c<=' ')c=read();boolean neg=(c=='-');if(neg)c=read();do{ret=ret*10+c-'0';}while((c=read())>='0'&&c<='9');if(neg)return-ret;return ret;}    public long nextLong()throws IOException{long ret=0;byte c=read();while(c<=' ')c=read();boolean neg=(c=='-');if(neg)c=read();do{ret=ret*10+c-'0';}while((c=read())>='0'&&c<='9');if(neg)return-ret;return ret;}    public double nextDouble()throws IOException{double ret=0,div=1;byte c=read();while(c<=' ')c=read();boolean neg=(c=='-');if(neg)c=read();do{ret=ret*10+c-'0';}while((c=read())>='0'&&c<='9');if(c=='.'){while((c=read())>='0'&&c<='9'){ret+=(c-'0')/(div*=10);}}        if(neg)return-ret;return ret;}    private void fillBuffer()throws IOException{bytesRead=din.read(buffer,bufferPointer=0,IO_BUFFERS);if(bytesRead==-1)buffer[0]=-1;}    private byte read()throws IOException{if(bufferPointer==bytesRead)fillBuffer();return buffer[bufferPointer++];}    public void close()throws IOException{if(din==null)return;din.close();}    int[]fillIntegerArray(int n)throws IOException{int[]array=new int[n];for(int i=0;i<n;i++)array[i]=nextInt();return array;}    long[]fillLongArray(int n)throws IOException{long[]array=new long[n];for(int i=0;i<n;i++)array[i]=nextLong();return array;}}
}