Shohag has an integer sequence a_1, a_2, …, a_n. He can perform the following operation any number of times (possibly, zero):

  * Select any positive integer k (it can be different in different operations). 
  * Choose any position in the sequence (possibly the beginning or end of the sequence, or in between any two elements) and insert k into the sequence at this position. 
  * This way, the sequence a changes, and the next operation is performed on this changed sequence. 



For example, if a=[3,3,4] and he selects k = 2, then after the operation he can obtain one of the sequences [\underline{2},3,3,4], [3,\underline{2},3,4], [3,3,\underline{2},4], or [3,3,4,\underline{2}].

Shohag wants this sequence to satisfy the following condition: for each 1 ≤ i ≤ |a|, a_i ≤ i. Here, |a| denotes the size of a.

Help him to find the minimum number of operations that he has to perform to achieve this goal. We can show that under the constraints of the problem it's always possible to achieve this goal in a finite number of operations.

Input

The first line contains a single integer t (1 ≤ t ≤ 200) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 100) — the initial length of the sequence.

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the elements of the sequence.

Output

For each test case, print a single integer — the minimum number of operations needed to perform to achieve the goal mentioned in the statement.

Example

Input


4
3
1 3 4
5
1 2 5 7 4
1
1
3
69 6969 696969


Output


1
3
0
696966

Note

In the first test case, we have to perform at least one operation, as a_2=3>2. We can perform the operation [1, 3, 4] → [1, \underline{2}, 3, 4] (the newly inserted element is underlined), now the condition is satisfied.

In the second test case, Shohag can perform the following operations:

[1, 2, 5, 7, 4] → [1, 2, \underline{3}, 5, 7, 4] → [1, 2, 3, \underline{4}, 5, 7, 4] → [1, 2, 3, 4, 5, \underline{3}, 7, 4].

In the third test case, the sequence already satisfies the condition.
1
39
481199252 336470888 634074578 642802746 740396295 773386884 579721198 396628655 503722503 971207868 202647942 2087506 268792718 46761498 443917727 16843338 125908043 691952768 717268783 787375312 150414369 693319712 519096230 45277106 856168102 762263554 674936674 407246545 274667941 279198849 527268921 155191459 421436316 536134606 286802932 140515506 646837311 233465964 451394766

971207858

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.io.*;
import java.util.*;
import java.text.DecimalFormat;
import java.math.*;

public class Main {

static int  mod = 1000000007;
/*****************code By Priyanshu *******************************************/ 

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;


        public FastReader()
        {
            br = new BufferedReader(
                new InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() { return Integer.parseInt(next()); }

        long nextLong() { return Long.parseLong(next()); }



        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    // this > other return +ve
    // this < other return -ve
    // this == other return 0
     public static class Pair implements Comparable<Pair> {
      long st;
      long et;

      public Pair(long st, long et) {
         this.st = st;
         this.et = et;
      }

      public int compareTo(Pair other) {
         if (this.st != other.st) {
            return (int)(this.st - other.st);
         } else {
            return (int)(this.et - other.et);
         }
      }
   }

    static long fastPower(long a, long b, int n) {
            
            long res = 1;
            
            while ( b > 0) {
                
                if ( (b&1) != 0) {
                    res = (res * a % n) % n;
                }
                
                a = (a % n * a % n) % n;
                b =  b >> 1;
            }
            
            return res;
            
        }

     // function to find
    // the rightmost set bit
    static int PositionRightmostSetbit(int n)
    {
        // Position variable initialize
        // with 1 m variable is used to
        // check the set bit
        int position = 1;
        int m = 1;
 
        while ((n & m) == 0) {
 
            // left shift
            m = m << 1;
            position++;
        }
        return position;
    }
    
         // used for swapping ith and jth elements of array
      // public static void swap(int[] arr, int i, int j) {
      //   int temp = arr[i];
      //   arr[i] = arr[j];
      //   arr[j] = temp;
      // }
        public static void swap(long i, long j) {
        long temp = i;
        i = j;
        j = temp;
      }


    static boolean palindrome(String s) {
        return new StringBuilder(s).reverse().toString().equals(s);
    }
    
  static boolean isPerfectSquare(double x)
    {
            double sr = Math.sqrt(x);
            return ((sr * sr) == x);     
    }


 public static long gcd(long a, long b)
    {
      if (b == 0)
        return a;
      return gcd(b, a % b);
    }
    
   

   static int nod(long l) {
       if(l>=1000000000000000000l) return 19;
       if(l>=100000000000000000l) return 18;
       if(l>=10000000000000000l) return 17;
       if(l>=1000000000000000l) return 16;
       if(l>=100000000000000l) return 15;
       if(l>=10000000000000l) return 14;
       if(l>=1000000000000l) return 13;
       if(l>=100000000000l) return 12;
       if(l>=10000000000l) return 11;
       if(l>=1000000000) return 10;
       if(l>=100000000) return 9;
       if(l>=10000000) return 8;
       if(l>=1000000) return 7;
       if(l>=100000) return 6;
       if(l>=10000) return 5;
       if(l>=1000) return 4;
       if(l>=100) return 3;
       if(l>=10) return 2;
       return 1;
    }
      //Arrays.sort(a,(c,d) -> Integer.compare(c[0],d[0]));

    
    public static boolean areAllBitsSet(int n )
    {
        // all bits are not set
        if (n == 0)
            return false;
     
        // if true, then all bits are set
        if (((n + 1) & n) == 0)
            return true;
     
        // else all bits are not set
        return false;
    }

     public static long[] sort(long[] arr) {
        List<Long> temp = new ArrayList();
        for (long i : arr) temp.add(i);
        Collections.sort(temp);
        int start = 0;
        for (long i : temp) arr[start++] = i;
        return arr;
    }
   
 

        public static int[] radixSort2(int[] a)
    {
        int n = a.length;
        int[] c0 = new int[0x101];
        int[] c1 = new int[0x101];
        int[] c2 = new int[0x101];
        int[] c3 = new int[0x101];
        for(int v : a) {
            c0[(v&0xff)+1]++;
            c1[(v>>>8&0xff)+1]++;
            c2[(v>>>16&0xff)+1]++;
            c3[(v>>>24^0x80)+1]++;
        }
        for(int i = 0;i < 0xff;i++) {
            c0[i+1] += c0[i];
            c1[i+1] += c1[i];
            c2[i+1] += c2[i];
            c3[i+1] += c3[i];
        }
        int[] t = new int[n];
        for(int v : a)t[c0[v&0xff]++] = v;
        for(int v : t)a[c1[v>>>8&0xff]++] = v;
        for(int v : a)t[c2[v>>>16&0xff]++] = v;
        for(int v : t)a[c3[v>>>24^0x80]++] = v;
        return a;
    } 

    public static void print( int arr[] ){
        Arrays.stream(arr).forEach(str -> System.out.print(str + " "));
    }

    static boolean isPowerOfTwo (int x)
    {
      /* First x in the below expression is 
        for the case when x is 0 */
        return x!=0 && ((x&(x-1)) == 0);
          
    }

   

  static class Help {
    int index;
    int val;
    int res ;
    //Constructor
    Help(int i, int v) {
      index = i;
      val = v;
      res = 0;
    }
  }
 


  public static void main(
        String[] args)
    {
        try {
            System.setIn(new FileInputStream("input.txt"));
            System.setOut(new PrintStream(new FileOutputStream("output.txt")));
        } catch (Exception e) {
            System.err.println("Error");
        }
         
       FastReader sc = new FastReader();
    
        int t = Integer.parseInt(sc.next());
      // int t = 1;
      

       // StringBuilder ans = new StringBuilder();
  //  ArrayList<Integer> a = new ArrayList<>();
    
   while(t-->0){
  

   int n  = sc.nextInt();
    int a[] = new int[n+1];
    int diff = 0;
   for (int i = 1;i <=n ;i++) {
     a[i] = sc.nextInt();
     if(a[i] <= i) continue;
     diff = Math.max(Math.abs(i - a[i]),diff);
   }
   System.out.println(diff);
    








    }
  }
}






//code By Priyanshu 

