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.*;
import java.text.*;
import java.lang.*;
import java.math.*;
 
public class Main{
    static ArrayList[] a = new ArrayList[200001];
 
    public void solve () throws IOException  {
       
    	InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int t  = in.nextInt();
        outer :
        while(t-- > 0) {
        	int n = in.nextInt();
        	long a[] = new long [n + 1];
        	for(int i = 0 ; i < n ; i ++) {
        		a[i] = in.nextLong();
        	}
        	boolean pre[] = new boolean [n + 1];
        	boolean  suf[] = new boolean  [n + 1];
        	pre[0] = (a[0] >= 0);
        	for(int i = 1 ; i < n ; i++)
        	{
        		pre[i] = (a[i] >= i ) & pre[i - 1];
        	}
        	suf[n - 1] = a[n - 1] >= 0;
        	for(int i = n - 2 ; i >= 0 ; i--) {
        		suf[i] = (a[i] >= (n - 1 - i))&suf[i + 1];
        	}
        	for(int i = 0 ; i < n ; i++) {
        		if(pre[i] && suf[i])
        		{
        			pw.println("Yes");
        			continue outer;
        		}
        	}
        	pw.println("No");
        }
        pw.flush();
        pw.close();
    }
    public static void main(String[] args) throws Exception {
        
        
        new Thread(null,new Runnable() {
            public void run() {
                    try {
                        new Main().solve();
                    } catch (FileNotFoundException e) {
                        // TODO Auto-generated catch block
                        e.printStackTrace();
                    } catch (IOException e) {
						// TODO Auto-generated catch block
						e.printStackTrace();
					}
            } 
        },"1",1<<26).start();
        
        
    }
   
    static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
        }
        
        static class InputReader 
        {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) 
        {
            this.stream = stream;
        }
        public int snext() 
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() 
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) 
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) 
            {
                a[i] = nextInt();
            }
            return a;
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() 
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
        public static long mod = 1000000007;
        public static int d;
        public static int p;
        public static int q;
        public void extended(int a,int b) {
            if(b==0) {
                d=a;
                p=1;
                q=0;
            }
            else
            {
                extended(b,a%b);
                int temp=p;
                p=q;
                q=temp-(a/b)*q;
            }
        }
       
        
        public static long binaryExponentiation(long x,long n)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static long[] shuffle(long[] a,Random gen)
        {
            int n = a.length;
            for(int i=0;i<n;i++)
            {
                int ind = gen.nextInt(n-i)+i;
                long temp = a[ind];
                a[ind] = a[i];
                a[i] = temp;
            }
            return a;
        }
        
        public static void swap(int a, int b){
            int temp = a;
            a = b;
            b = temp;
        }
        
        public static HashSet<Integer> primeFactorization(int n)
        {
            HashSet<Integer> a =new HashSet<Integer>();
            for(int i=2;i*i<=n;i++)
            {
                while(n%i==0)
                {
                    a.add(i);
                    n/=i;
                }
            }
            if(n!=1)
                a.add(n);
            return a;
        }
        
        public static void sieve(boolean[] isPrime,int n)
        {
            for(int i=1;i<n;i++)
                isPrime[i] = true;
            
            isPrime[0] = false;
            isPrime[1] = false;
            
            for(int i=2;i*i<n;i++)
            {
                if(isPrime[i] == true)
                {
                    for(int j=(2*i);j<n;j+=i)
                        isPrime[j] = false;
                }
            }
        }
        
        public static long GCD(long n,long m)
        {
            if(m==0)
                return n;
            else
                return GCD(m,n%m);
        }
        public static long LCM (long a,long b) {
            return ((a*b)/(GCD(a,b)));
        }
        
        static class pair implements Comparable<pair>
        {
            Integer y , x ;
            
            pair(int l,Integer y)
            {
                this.x=l;
                this.y=y;
            }

           
            public int compareTo(pair o) {
                int result = x.compareTo(o.x);
                if(result==0)
                    result = y.compareTo(o.y);
                
                return result;
            }  
            
            public String toString()
            {
                return x+" "+y;
            }
            
            public boolean equals(Object o)
            {
                if (o instanceof pair)
                {
                    pair p = (pair)o;
                    return p.x == x && p.y == y ;
                }
                return false;
            }
            public int hashCode()
            {
                return new Long(x).hashCode()*3 + new Long(y).hashCode();
                
            }
        }
        public static int binaryExponentiation(int x,int n)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
       
        
        public static int modularExponentiation(int x,int n,int M)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result * x)%M;
                x=(x%M*x)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modularExponentiation(long x,long n,long M)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result%M * x%M)%M;
                x=(x%M * x%M)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modInverse(int A,int M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static long modInverse(long A,long M)
        {
            return modularExponentiation(A,M-2,M);
        }
        static class Segment{ 
    		int seg[]; 
    		int a[];
    		int lazy[];
    	    Segment (int n,int b[]){
    			seg=new int[4*n];
    			lazy=new int[4*n];
    			a=new int[b.length];
    			a=b.clone();
    		}
    	    public void build(int node,int start,int end) {
    	    	if(start==end) {
    	    		seg[node]=a[start];
    	    		return ;
    	    	}
    	    	int mid=(start+end)/2;
    	    	build(2*node+1,start,mid);
    	    	build(2*node+2,mid+1,end);
    	    	seg[node]=seg[2*node+1]+seg[2*node+2];
    	    }
    	    public void update(int node,int start,int end,int id,int val) {
    	    	if(start==end) {
    	    		seg[node]=a[start]=val;
    	    		return;
    	    	}
    	    	int mid=(start+end)/2;
    	    	if(id>=start && id<=mid) {
    	    		update(2*node+1,start,mid,id,val);
    	    	}
    	    	else
    	    		update(2*node+2,mid+1,end,id,val);
    	    	seg[node]=seg[2*node+1]+seg[2*node+2];
    	    }
    	    public int query(int node,int start,int end,int l,int r) {
    	    	if(l>end || r<start)
    	    		return 0;
    	    	if(start>=l && end<=r)
    	    		return seg[node];
    	    	
    	    	int  mid=(start+end)/2;
    	    	return (query(2*node+1,start,mid,l,r)+query(2*node+2,mid+1,end,l,r));
    	    }
    	    public void updateRange(int node,int start,int end,int l,int r,int val) {
    	    	if(lazy[node]!=0) {
	    			seg[node] += lazy[node];
    	    		if(start!=end) {
    	    			lazy[2*node+1]+=lazy[node];
    	    			lazy[2*node+2]+=lazy[node];
    	    		}
    	    		lazy[node]=0;
    	    	}
    	    	if(l>end || r<start)
    	    		return ;
    	    	if(start>=l && end<=r) {
    	    		seg[node] += val;
    	    		if(start!=end) {
    	    			lazy[2*node+1]+=val;
    	    			lazy[2*node+2]+=val;
    	    		}
    	    		lazy[node]=0;
    	    		return ;
    	    	}
    	    	int mid=(start+end)/2;
    	    	updateRange(2*node+1,start,mid,l,r,val);
    	    	updateRange(2*node+2,mid+1,end,l,r,val);
    	    	seg[node]=seg[2*node+1]+seg[2*node+2];
    	    }
    	    public int queryRange(int node,int start,int end,int l,int r) {
    	    	if(l>end || r<start)
    	    		return 0;
    	    	if(lazy[node]!=0) {
    	    		seg[node] += lazy[node];
    	    		if(start!=end) {
    	    			lazy[2*node+1]+=lazy[node];
    	    			lazy[2*node+2]+=lazy[node];
    	    		}
    	    		lazy[node]=0;
    	    	}
    	    	if(start>=l && end<=r)
    	    		return seg[node];
    	    	
    	    	int  mid=(start+end)/2;
    	    	return (queryRange(2*node+1,start,mid,l,r)+queryRange(2*node+2,mid+1,end,l,r));
    	    }
    	    
    	}
       
        
                    
         
}