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.io.*;
import java.util.*;
import java.math.*;
import java.lang.*;

public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        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 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 double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            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 boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(), "Main", 1 << 27).start();
    }

    static class Pair {
        int f;
        int s;
        int p;
        PrintWriter w;

        // int t;

        Pair(int f, int s) {
            // Pair(int f,int s, PrintWriter w){
            this.f = f;
            this.s = s;
            // this.p = p;
            // this.w = w;
            // this.t = t;

        }

        public static Comparator<Pair> wc = new Comparator<Pair>() {
            public int compare(Pair e1, Pair e2) {

                // 1 for swap
                if (Math.abs(e1.f) - Math.abs(e2.f) != 0) {
                    // e1.w.println("**"+e1.f+" "+e2.f);
                    return (Math.abs(e1.f) - Math.abs(e2.f));
                } else {
                    // e1.w.println("##"+e1.f+" "+e2.f);
                    return (Math.abs(e1.s) - Math.abs(e2.s));
                }

            }
        };
    }

    public static ArrayList<Integer> sieve(int N) {
        int i, j, flag;

        ArrayList<Integer> p = new ArrayList<Integer>();

        for (i = 1; i < N; i++) {

            if (i == 1 || i == 0)
                continue;

            flag = 1;

            for (j = 2; j <= i / 2; ++j) {
                if (i % j == 0) {
                    flag = 0;
                    break;
                }
            }
            if (flag == 1) {
                p.add(i);
            }
        }
        return p;
    }

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

    //// recursive dfs
    public static int dfs(int s, ArrayList<Integer>[] g, long[] dist, boolean[] v, PrintWriter w, int p) {
        v[s] = true;
        int ans = 1;
        // int n = dist.length - 1;
        int t = g[s].size();
        // int max = 1;
        for (int i = 0; i < t; i++) {
            int x = g[s].get(i);
            if (!v[x]) {
                // dist[x] = dist[s] + 1;
                ans = Math.min(ans, dfs(x, g, dist, v, w, s));
            } else if (x != p) {
                // w.println("* " + s + " " + x + " " + p);
                ans = 0;
            }
        }
        // max = Math.max(max,(n-p));
        return ans;
    }

    //// iterative BFS
    public static int bfs(int s, ArrayList<Integer>[] g, long[] dist, boolean[] b, PrintWriter w, int p) {
        b[s] = true;
        int siz = 1;
        // dist--;
        Queue<Integer> q = new LinkedList<>();
        q.add(s);
        while (q.size() != 0) {
            int i = q.poll();
            Iterator<Integer> it = g[i].listIterator();
            int z = 0;
            while (it.hasNext()) {
                z = it.next();
                if (!b[z]) {
                    b[z] = true;
                    // dist--;
                    dist[z] = dist[i] + 1;
                    // siz++;
                    q.add(z);
                } else if (z != p) {
                    siz = 0;
                }
            }

        }
        return siz;
    }

    public static int lower(int key, int[] a) {
        int l = 0;
        int r = a.length - 1;
        int res = 0;

        while (l <= r) {
            int mid = (l + r) / 2;

            if (a[mid] <= key) {
                l = mid + 1;
                res = mid + 1;
            } else {
                r = mid - 1;
            }
        }

        return res;
    }

    public static long power(long x, long y, long m) {
        if (y == 0)
            return 1;

        long p = power(x, y / 2, m) % m;
        p = (p * p) % m;

        if (y % 2 == 0)
            return p;
        else
            return (x * p) % m;
    }

    //////////////////////////////////////////////////////////////////////////////////////////////////////
    //////////////////////////////////////////////////////////////////////////////////////////////////////
    // code here
    int[] parent;
    int[] dist;
    int[] height;
    boolean[] vis;
    ArrayList<Integer>[] g;
    int[] col;

    public void run() {

        InputReader sc = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);
        int defaultValue = 0;
        int mod = 1000000007;
        int oo = (int) 1e9;

        int test = 1;
        test = sc.nextInt();
        while (test-- > 0) {
            int n = sc.nextInt();
            int[] a = new int[n];
            int[] dp = new int[n];

            for (int i = 0; i < n; i++) {
                a[i] = sc.nextInt();
            }
            long ans = 0;

            for (int i = 0; i < n; i++) {
                if (i > 0)
                    dp[i] += dp[i - 1];
                int z = a[i] + dp[i];
                // w.print(z + " ");
                ans += Math.max(z - 1, 0);
                // if(a[i]>0){
                // int x = Math.min(n-1,a[i]+1);
                // dp[x]++;
                // dp[i+1]--;
                // }
                // else{
                if (i == n - 1 || (a[i] == 1 && z == 1))
                    continue;
                int y = Math.max(1 - z, 1);
                int x = Math.min(n - 1, a[i] + i) + 1;

                if (x < n)
                    dp[x] += 1;
                if (z >= 1) {
                    if (i < n - 2)
                        dp[i + 2] -= 1;
                } else {
                    dp[i + 1] -= y;
                    if (i < n - 2)
                        dp[i + 2] += (y - 1);
                }
                // a[i] = z;
                // for (int j = 0; j < n; j++) {

                // w.print(a[j] + " ");
                // }
                // w.println("");
                // }
                // for (int j = 0; j < n; j++) {

                // w.print(dp[j] + " ");
                // }
                // w.println("");
            }
            // w.println("");

            w.println(ans);
        }

        w.flush();
        w.close();

    }

}
