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 java.util.*;
import java.lang.*;
import java.io.*;  
public class Main 
{
/*
    HashMap<> map=new HashMap<>();
    TreeMap<> map=new TreeMap<>();
    map.put(p,map.getOrDefault(p,0)+1);
    for(Map.Entry<> mx:map.entrySet()){
          int v=mx.getValue(),k=mx.getKey();
    }for (int i = 1; i <= 1000; i++)
    fac[i] = fac[i - 1] * i % mod;
    ArrayList<Pair<Character,Integer>> l=new ArrayList<>();
    ArrayList<> l=new ArrayList<>();
    HashSet<> has=new HashSet<>();
    PriorityQueue<Integer> pq=new PriorityQueue<>(new Comparator<Integer>(){
                public int compare(Integer a,Integer b){
                      return Integer.compare(b,a);
                }
                });
    Arrays.sort(ar,new Comparator<int[]>() {
    public int compare(int[] a, int[] b) {
        return Double.compare(a[0], b[0]);
    }
    });*/ 
    PrintWriter out;
    FastReader sc;
    long mod=(long)(1e9+7);
    int maxint= Integer.MAX_VALUE;
    int minint= Integer.MIN_VALUE;
    long maxlong=Long.MAX_VALUE;
    long minlong=Long.MIN_VALUE;
    
    
    /******************************************************************************************
     *****************************************************************************************/
    public void sol(){
          int n=ni();
          long[] ar=new long[n];
          for(int i=0;i<n;i++)ar[i]=nl();
          long ans=0;
          long[] val=new long[n];
          for(int i=0;i<n;i++){
                long temp=val[i];
                if(temp<ar[i]-1){
                      ans+=(ar[i]-1-temp);
                      temp+=(ar[i]-1-temp);
                }if(i!=n-1)val[i+1]+=(temp-ar[i]+1);
                if(i+2<n){
                      for(int j=i+2;j<n&&j<=(i+ar[i]);j++)val[j]++;
                }
          }pl(ans);
    }
    public static void main(String[] args) 
	{ 
	      Main g=new Main();
		g.out=new PrintWriter(System.out);
		g.sc=new FastReader();
		int t=g.ni();
            // int t=1;
		while(t-->0)
		g.sol();
		g.out.flush();
	}
	
	
	/****************************************************************************************
     *****************************************************************************************/
	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; 
		} 
	} public int ni(){
	      return sc.nextInt();
	}public long nl(){
	      return sc.nextLong();
	}public double nd(){
	      return sc.nextDouble();
	}public char[] rl(){
	      return sc.nextLine().toCharArray();
	}public String rl1(){
	      return sc.nextLine();
	}
	public void pl(Object s){
	      out.println(s);
	}public void ex(){
	      out.println();
	}
	public void pr(Object s){
	      out.print(s);
	}public String next(){
	      return sc.next();
	}public long abs(long x){
	      return Math.abs(x);
	}
	public int abs(int x){
	      return Math.abs(x);
	}
	public double abs(double x){
	      return Math.abs(x);
	}
      public long pow(long x,long y){
            return (long)Math.pow(x,y);
      }
      public int pow(int x,int y){
            return (int)Math.pow(x,y);
      }
      public double pow(double x,double y){
            return Math.pow(x,y);
      }public long min(long x,long y){
            return (long)Math.min(x,y);
      }
      public int min(int x,int y){
            return (int)Math.min(x,y);
      }
      public double min(double x,double y){
            return Math.min(x,y);
      }public long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}public long lcm(long a, long b) {
            return (a / gcd(a, b)) * b;
      }
       void sort1(int[] a) {
		ArrayList<Integer> l = new ArrayList<>();
		for (int i : a) {
			l.add(i);
		}
		Collections.sort(l,Collections.reverseOrder());
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}
	 void sort(int[] a) {
		ArrayList<Integer> l = new ArrayList<>();
		for (int i : a) {
			l.add(i);
		}
		Collections.sort(l);
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}void sort(long[] a) {
		ArrayList<Long> l = new ArrayList<>();
		for (long i : a) {
			l.add(i);
		}
		Collections.sort(l);
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}void sort1(long[] a) {
		ArrayList<Long> l = new ArrayList<>();
		for (long i : a) {
			l.add(i);
		}
		Collections.sort(l,Collections.reverseOrder());
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}
	void sort(double[] a) {
		ArrayList<Double> l = new ArrayList<>();
		for (double i : a) {
			l.add(i);
		}
		Collections.sort(l);
		for (int i = 0; i < a.length; i++) {
			a[i] = l.get(i);
		}
	}int  swap(int a,int b){
	      return a;
	}long  swap(long a,long b){
	      return a;
	}double  swap(double a,double b){
	      return a;
	}
	boolean isPowerOfTwo (int x) 
      { 
            return x!=0 && ((x&(x-1)) == 0);     
      }boolean isPowerOfTwo (long x) 
      { 
            return x!=0 && ((x&(x-1)) == 0);     
      }public long max(long x,long y){
            return (long)Math.max(x,y);
      }
      public int max(int x,int y){
            return (int)Math.max(x,y);
      }
      public double max(double x,double y){
            return Math.max(x,y);
      }long sqrt(long x){
            return (long)Math.sqrt(x);
      }int sqrt(int x){
            return (int)Math.sqrt(x);
      }void input(int[] ar,int n){
            for(int i=0;i<n;i++)ar[i]=ni();
      }void input(long[] ar,int n){
            for(int i=0;i<n;i++)ar[i]=nl();
      }void fill(int[] ar,int k){
            Arrays.fill(ar,k);
      }void yes(){
            pl("YES");
      }void no(){
            pl("NO");
      }
    int[] sieve(int n) 
    { 
        boolean prime[] = new boolean[n+1]; 
        int[] k=new int[n+1];
        for(int i=0;i<=n;i++) {
            prime[i] = true; 
            k[i]=i;
        }
          
        for(int p = 2; p <=n; p++) 
        { 
            if(prime[p] == true) 
            { 
               // sieve[p]=p;
                for(int i = p*2; i <= n; i += p) {
                    prime[i] = false; 
                  //  sieve[i]=p;
                    while(k[i]%(p*p)==0){
                          k[i]/=(p*p);
                    }
                }
            } 
        }return k;
    }
    int strSmall(int[] arr, int target)  
    {  
        int start = 0, end = arr.length-1;  
        int ans = -1;  
        while (start <= end) {  
            int mid = (start + end) / 2;   
            if (arr[mid] >= target) {  
                end = mid - 1;  
            }   
            else {  
                ans = mid;  
                start = mid + 1;  
            }  
        }  
        return ans;  
    } int strSmall(ArrayList<Integer> arr, int target)  
    {  
        int start = 0, end = arr.size()-1;  
        int ans = -1;  
        while (start <= end) {  
            int mid = (start + end) / 2;   
            if (arr.get(mid) > target) {  
                start = mid + 1; 
                ans=start;
            }   
            else {
                end = mid - 1;  
            }  
        }  
        return ans;  
    }long mMultiplication(long a,long b) 
    { 
        long res = 0;    
        a %= mod; 
  
        while (b > 0)  
        {  
            if ((b & 1) > 0)  
            { 
                res = (res + a) % mod; 
            }  
            a = (2 * a) % mod; 
  
            b >>= 1;  
        } 
        return res; 
    }long nCr(int n, int r,
                             long p)
    {
 
          if (n<r) 
              return 0;
        if (r == 0)
            return 1;
            long[] fac = new long[n + 1];
        fac[0] = 1;
 
        for (int i = 1; i <= n; i++)
            fac[i] = fac[i - 1] * i % p;
        return (fac[n] * modInverse(fac[r], p)
                % p * modInverse(fac[n - r], p)
                % p)
            % p;
    }long power(long x, long y, long p)
    {
        long res = 1;
        x = x % p;
 
        while (y > 0) {
            if (y % 2 == 1)
                res = (res * x) % p;
            y = y >> 1; 
            x = (x * x) % p;
        }
 
        return res;
    }long modInverse(long n, long p)
    {
        return power(n, p - 2, p);
    }
      public static class Pair implements Comparable<Pair> {
		int x;
		int y;
 
		public Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}
 
		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 Double(x).hashCode() * 31 + new Double(y).hashCode();
		}
 
		public int compareTo(Pair other) {
			if (this.x == other.x) {
				return Long.compare(this.y, other.y);
			}
			return Long.compare(this.x, other.x);
		}
      }
	 
} 