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.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.security.KeyStore.Entry;
import java.text.DecimalFormat;
import java.util.*;
import java.util.regex.Matcher;
import java.util.regex.Pattern;
 
import javax.net.ssl.SSLContext;
 
 
 
public class Main
{ 
   static long mod=(long)(1e+9 + 7);
   static int[] sieve;
   static ArrayList<Integer> primes;
   static long min=Long.MAX_VALUE;
   
   public static void main(String[] args) throws java.lang.Exception
   {	  	
	     fast s = new fast();
	     PrintWriter out=new PrintWriter(System.out);
	     StringBuilder fans=new StringBuilder("");

	     int t=s.nextInt();
	     
	     while(t>0)
	    	 {
	    		 int n=s.nextInt();
	    		 long a[]=new long[n];
	    		 
	    		 
	    		 for(int i=0;i<n;i++) a[i]=s.nextLong();
	    		 
	    		 if(n==1) {System.out.println("Yes");t--;continue;}
	    		 int flag1=1;
	    		 int flag2=1;
	    		 
	    		 for(int i=1;i<n;i++)
	    			 if(a[i]<=a[i-1]) flag1=0;
	    		 for(int i=n-2;i>=0;i--)
	    			 if(a[i]<=a[i+1]) flag2=0;
	    		 
	    		 int right_pos[]=new int[n];
	    		 int left_pos[]=new int[n];
	    		 
	    		 left_pos[0]=1;
	    		 right_pos[n-1]=1;
	    		 
	    		 int k=1;
	    		 
	    		 for(int i=n-2;i>=0;i--)
	    			 {
	    			    if(a[i]>=k && right_pos[i+1]==1) right_pos[i]=1;
	    			    k++;
	    			 }
	    		 
	    		 k=1;
	    		 for(int i=1;i<n;i++)
	    			 {
	    				 if(a[i]>=k && left_pos[i-1]==1) left_pos[i]=1;
	                     k++;
	    			 }
	    		 
	    		 int flag=0;
	    		 for(int i=1;i<n-1;i++)
	    			 {
	    				 if(a[i]>=n-i-1 && (a[i]>=i) && left_pos[i-1]==1 && right_pos[i+1]==1) flag=1;
	    			 }
	    		 
	    		 if(a[0]>=n-1 && a[0]>=0 && right_pos[1]==1) flag=1;
	    		 if(a[n-1]>=0 && a[n-1]>=n-1 && left_pos[n-2]==1) flag=1;
	    		 
	    		 //System.out.println(flag+" "+flag1+" "+flag2);
	    		 if(flag==1 || flag1==1 || flag2==1) System.out.println("Yes");
	    		 else System.out.println("No");
	    		 t--;
	    	 }
   }
  
 
 
static class fast {   
	    private InputStream i;
		private byte[]  buf = new byte[1024];
		private int curChar;
		
		private int numChars;
		
		//Return floor log2n
		public static long log2(long bits) // returns 0 for bits=0
			{
			    int log = 0;
			    if( ( bits & 0xffff0000 ) != 0 ) { bits >>>= 16; log = 16; }
			    if( bits >= 256 ) { bits >>>= 8; log += 8; }
			    if( bits >= 16  ) { bits >>>= 4; log += 4; }
			    if( bits >= 4   ) { bits >>>= 2; log += 2; }
			    return log + ( bits >>> 1 );
			}
		
		public static boolean next_permutation(int a[])
		   {
			   int i=0,j=0;int index=-1;	   
			   int n=a.length;
			   
			   for(i=0;i<n-1;i++)
				   if(a[i]<a[i+1]) index=i;
			   
			   if(index==-1) return false;
			   i=index;
 
			  
			   for(j=i+1;j<n && a[i]<a[j];j++);
 
			   int temp=a[i];
			   a[i]=a[j-1];
			   a[j-1]=temp;
			   	   
			   for(int p=i+1,q=n-1;p<q;p++,q--)
			   {
				   temp=a[p];
				   a[p]=a[q];
				   a[q]=temp;
			   }
			   
			   return true;
		   }
		   
		   
		public static void division(char ch[],int divisor)
		   {
			   int div=Character.getNumericValue(ch[0]); int mul=10;int remainder=0;
			   StringBuilder quotient=new StringBuilder("");
			   for(int i=1;i<ch.length;i++)
			   {
				   div=div*mul+Character.getNumericValue(ch[i]);	
				   if(div<divisor) {quotient.append("0");continue;}
				   quotient.append(div/divisor);
				   div=div%divisor;mul=10;
				   
			   } 
			   remainder=div;
			   while(quotient.charAt(0)=='0')quotient.deleteCharAt(0);	   
			   System.out.println(quotient+" "+remainder);	  
		   }
		
		public static void sieve(int size)
		{
			sieve=new int[size+1];
			
			primes=new ArrayList<Integer>();
			
			sieve[1]=1;
			
			for(int i=2;i*i<=size;i++)
			{
				if(sieve[i]==0)
				 {
					for(int j=i*i;j<size;j+=i) {sieve[j]=1;}
				 }
			}
			
			for(int i=2;i<=size;i++)
			{
				if(sieve[i]==0) primes.add(i);
			}
		}
		
		public static long pow(long n, long b, long MOD)
		   {
		       long x=1;long y=n; 
		       while(b > 0)
		       {
		           if(b%2 == 1)
		           {
		               x=x*y;
		               if(x>MOD) x=x%(MOD);
		           }
		           y = y*y;
		           if(y>MOD) y=y%(MOD); 
		           b >>= 1;
		       }
		       return x;
		   }
 
 
		public static long mod_inv(long n,long mod)
		{
			return pow(n,mod-2,mod);
		}
		
		//Returns index of highest number less than or equal to key
		 public static int upper(long[] a,int length,long key)
		 {
			    int low = 0;
		        int high = length-1;
		        int ans=-1;
		        
		        while (low <= high) {
		            int mid = (low + high) / 2;
		            if (key >= a[mid]) {
		                ans=mid;
		            	low = mid+1;
		            } else if(a[mid]>key){
		                high = mid - 1;
		            }
		        }
		        return ans;
		}
		
		//Returns index of least number greater than or equal to key
		 public static int lower(long[] a,int length,long key)
		 {
			    int low = 0;
		        int high = length-1;
		        int ans=-1;
		        
		        while (low <= high) {
		            int mid = (low + high) / 2;
		            if (key<=a[mid]) {
		                ans=mid;
		            	high = mid-1;
		            }
		            else{
		            		low=mid+1;
		            	}
		        }
		        return ans;
		} 
		   
		public long gcd(long r,long ans)
		{
			if(r==0) return ans;
			return gcd(ans%r,r);
		}
		public fast() {
			this(System.in);
		}
		public fast(InputStream is) {
			i = is;
		}
		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = i.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}
		public String nextString() {
     		int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		public boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
		public boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
 
	}	
}