There is a trampoline park with n trampolines in a line. The i-th of which has strength S_i.

Pekora can jump on trampolines in multiple passes. She starts the pass by jumping on any trampoline of her choice. 

If at the moment Pekora jumps on trampoline i, the trampoline will launch her to position i + S_i, and S_i will become equal to max(S_i-1,1). In other words, S_i will decrease by 1, except of the case S_i=1, when S_i will remain equal to 1. 

If there is no trampoline in position i + S_i, then this pass is over. Otherwise, Pekora will continue the pass by jumping from the trampoline at position i + S_i by the same rule as above.

Pekora can't stop jumping during the pass until she lands at the position larger than n (in which there is no trampoline). Poor Pekora!

Pekora is a naughty rabbit and wants to ruin the trampoline park by reducing all S_i to 1. What is the minimum number of passes she needs to reduce all S_i to 1?

Input

The first line contains a single integer t (1 ≤ t ≤ 500) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 5000) — the number of trampolines.

The second line of each test case contains n integers S_1, S_2, ..., S_n (1 ≤ S_i ≤ 10^9), where S_i is the strength of the i-th trampoline.

It's guaranteed that the sum of n over all test cases doesn't exceed 5000.

Output

For each test case, output a single integer — the minimum number of passes Pekora needs to do to reduce all S_i to 1.

Example

Input


3
7
1 4 2 2 2 2 2
2
2 3
5
1 1 1 1 1


Output


4
3
0

Note

For the first test case, here is an optimal series of passes Pekora can take. (The bolded numbers are the positions that Pekora jumps into during these passes.)

  * [1,4,2,2,2,2,2] 
  * [1,4,1,2,1,2,1] 
  * [1,3,1,2,1,1,1] 
  * [1,2,1,2,1,1,1] 



For the second test case, the optimal series of passes is show below.

  * [2,3] 
  * [1,3] 
  * [1,2] 



For the third test case, all S_i are already equal to 1.
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;
import java.io.*;
import java.util.*;

public class A
{
    static int n;
    static int[] arr;
    static char[] s;
    public static void main(String[] args) throws IOException
    {
        f = new Flash();
        out = new PrintWriter(System.out);
        
        int T = ni();
        for(int tc = 1; tc <= T; tc++){
            n = ni(); arr = arr(n); sop(fn());
        }
        
        out.flush(); out.close();
    }
    
    static long fn()
    {
    	//https://codeforces.com/blog/entry/88248?#comment-766558
    	//this is O(N)
        long ans = 0;
        long[] times = new long[n];
        for(int i = 0; i < n; i++) {
        	if(i > 0) times[i] += times[i-1];
        	
        	ans += max(0, arr[i]-1-times[i]);
        	
        	if(i+1 < n && times[i] > (arr[i]-1)) {
        		long count = times[i] - (arr[i]-1);
        		times[i+1] += count;
        		if(i+2 < n) times[i+2] -= count;
        	}
        	
        	int mx = min(n-1, i+arr[i]);
        	if(i+2 < n) times[i+2]++;
        	if(mx+1 < n) times[mx+1]--;
        }
        
        return ans;
    }
    
    static Flash f;
    static PrintWriter out;
    static final long mod = (long)1e9+7;
    static final long inf = Long.MAX_VALUE;
    static final int _inf = Integer.MAX_VALUE;
    static final int maxN = (int)5e5+5;
    static long[] fact, inv;
    
    static void sort(int[] a){
        List<Integer> A = new ArrayList<>();
        for(int i : a) A.add(i);
        Collections.sort(A);
        for(int i = 0; i < A.size(); i++) a[i] = A.get(i);
    }
    
    static void sort(long[] a){
        List<Long> A = new ArrayList<>();
        for(long i : a) A.add(i);
        Collections.sort(A);
        for(int i = 0; i < A.size(); i++) a[i] = A.get(i);
    }
    
    static void print(int[] a){
        StringBuilder sb = new StringBuilder();
        for(int i = 0; i < a.length; i++) sb.append(a[i] + " ");
        sop(sb);
    }
    
    static void print(long[] a){
        StringBuilder sb = new StringBuilder();
        for(int i = 0; i < a.length; i++) sb.append(a[i] + " ");
        sop(sb);
    }
    
    static int swap(int itself, int dummy){return itself;}
    static long swap(long itself, long dummy){return itself;}
    static void sop(Object o){out.println(o);}
    static int ni(){return f.ni();}
    static long nl(){return f.nl();}
    static double nd(){return f.nd();}
    static String next(){return f.next();}
    static String ns(){return f.ns();}
    static char[] nc(){return f.nc();}
    static int[] arr(int len){return f.arr(len);}
    static int gcd(int a, int b){if(b == 0) return a; return gcd(b, a%b);}
    static long gcd(long a, long b){if(b == 0) return a; return gcd(b, a%b);}
    static int lcm(int a, int b){return (a*b)/gcd(a, b);}
    static long lcm(long a, long b){return (a*b)/gcd(a, b);}
    
    static class Flash
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");
        
        String next(){
            while(!st.hasMoreTokens()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch(IOException e){
                    e.printStackTrace();
                }
            }
            
            return st.nextToken();
        }
        
        String ns(){
            String s = new String();
            try{
                s = br.readLine().trim();
            }catch(IOException e){
                e.printStackTrace();
            }
            
            return s;
        }
        
        int[] arr(int n){
            int[] a = new int[n];
            for(int i = 0; i < n; i++) a[i] = ni();
            return a;
        }
        
        char[] nc(){return ns().toCharArray();}
        int ni(){return Integer.parseInt(next());}
        long nl(){return Long.parseLong(next());}
        double nd(){return Double.parseDouble(next());}
    }
}