An important meeting is to be held and there are exactly n people invited. At any moment, any two people can step back and talk in private. The same two people can talk several (as many as they want) times per meeting.

Each person has limited sociability. The sociability of the i-th person is a non-negative integer a_i. This means that after exactly a_i talks this person leaves the meeting (and does not talk to anyone else anymore). If a_i = 0, the i-th person leaves the meeting immediately after it starts.

A meeting is considered most productive if the maximum possible number of talks took place during it.

You are given an array of sociability a, determine which people should talk to each other so that the total number of talks is as large as possible.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases.

The next 2t lines contain descriptions of the test cases.

The first line of each test case description contains an integer n (2 ≤ n ≤ 2 ⋅ 10^5) —the number of people in the meeting. The second line consists of n space-separated integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 2 ⋅ 10^5) — the sociability parameters of all people. 

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5. It is also guaranteed that the sum of all a_i (over all test cases and all i) does not exceed 2 ⋅ 10^5.

Output

Print t answers to all test cases.

On the first line of each answer print the number k — the maximum number of talks possible in a meeting.

On each of the next k lines print two integers i and j (1 ≤ i, j ≤ n and i ≠ j) — the numbers of people who will have another talk.

If there are several possible answers, you may print any of them.

Example

Input


8
2
2 3
3
1 2 3
4
1 2 3 4
3
0 0 2
2
6 2
3
0 0 2
5
8 2 0 1 1
5
0 1 0 0 6


Output


2
1 2
1 2
3
1 3
2 3
2 3
5
1 3
2 4
2 4
3 4
3 4
0
2
1 2
1 2
0
4
1 2
1 5
1 4
1 2
1
5 2
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

import static java.lang.Math.*;

public class Main {

    //------------------------------------------CONSTANTS---------------------------------------------------------------
    public static final int MOD = (int) (1e9 + 7);

    //---------------------------------------------I/0------------------------------------------------------------------

    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 static void print(String s) {
        System.out.println(s);
    }

    public static void main(String[] args) {
        FastReader sc = new FastReader();

        int t = 1;
        t = sc.nextInt();

        for(int i = 0; i<t; i++) {
            System.out.println(solve(sc));
        }
    }

    //------------------------------------------------SOLVE-------------------------------------------------------------

    public static String solve(FastReader sc) {
        int n = sc.nextInt();
        int[] a = new int[n];
        for (int i = 0; i<n; i++) {
            a[i] = sc.nextInt();
        }

        int talks = 0;

        TreeSet<Pair<Integer, Integer>> people = new TreeSet<>(new Comparator<>() {
            @Override
            public int compare(Pair<Integer, Integer> integerIntegerPair, Pair<Integer, Integer> t1) {
                return -integerIntegerPair.compareTo(t1);
            }
        });

        for (int i = 0; i<n; i++) {
            if (a[i] != 0) {
                people.add(new Pair<>(a[i], i+1));
            }
        }

        StringBuilder res = new StringBuilder("");

        while (people.size() > 2) {
            Pair<Integer, Integer> p1 = people.pollFirst();
            Pair<Integer, Integer> p2 = people.pollFirst();
            Pair<Integer, Integer> p3 = people.first();
            p1.a -= (p2.a - p3.a) + 1;
            talks += (p2.a - p3.a) + 1;
            for (int i = 0; i<(p2.a - p3.a) + 1; i++) {
                res.append(p1.b + " " + p2.b + "\n");
            }
            p2.a -= (p2.a - p3.a) + 1;
            if (p1.a > 0) {
                people.add(p1);
            }
            if (p2.a > 0) {
                people.add(p2);
            }
        }

        if (people.size() == 2) {
            Pair<Integer, Integer> p1 = people.pollFirst();
            Pair<Integer, Integer> p2 = people.pollFirst();
            talks += p2.a;
            for (int i = 0; i<p2.a; i++) {
                res.append(p1.b + " " + p2.b + "\n");
            }
        }
        res.insert(0, talks + "\n");

        return res.substring(0, res.length()-1);
    }

    public static boolean isOrdered(int[] a) {
        for (int i = 0; i<a.length-1; i++) {
            if (a[i] > a[i+1])
                return false;
        }

        return true;
    }

    public static void cycleShift(int[] a, int l, int r, int d) {
        for (int i = 0; i<d; i++) {
            int al = a[l];
            for (int j = l; j<r-1; j++) {
                a[j] = a[j+1];
            }
            a[r-1] = al;
        }
    }

    //-----------------------------------------------FUNCTIONS----------------------------------------------------------

    public static String printArray(int[] a) {
        StringBuilder r = new StringBuilder("");

        for(int i = 0; i<a.length; i++) {
            r.append(a[i] + " ");
        }
        return r.toString();
    }

    // first element that is not less than target
    public static int lowerBound(int[] arr, int begin, int end, int target) {
        while(begin < end) {
            int mid = begin + (end - begin) / 2;
            // When the element is less than the mid target
            if(arr[mid] < target)
                // begin to mid + 1, arr [begin] value is less than or equal target
                begin = mid + 1;
                // When the mid target element when greater than or equal
            else if(arr[mid] >= target)
                end = mid;
        }
        return begin;
    }

    // first element that is greater than target
    public static int upperBound(int[] arr, int begin, int end, int target) {
        while(begin < end) {
            int mid = begin + (end - begin) / 2;
            if(arr[mid] <= target)
                begin = mid + 1;
            else
                end = mid;
        }
        return begin;
    }

    // generate permutations (call search and access through permutations)
    public static class Permutations {
        List<List<Integer>> permutations = new ArrayList<>();
        List<Integer> permutation = new ArrayList<>();
        boolean[] taken;
        int[] a;

        public Permutations(int[] a) {
            this.a = a;
            taken = new boolean[a.length];
        }

        void search() {
            if (permutation.size()==a.length) {
                permutations.add(new ArrayList<>(permutation));
            } else {
                for (int i = 0; i<a.length; i++) {
                    if (taken[i]) {
                        continue;
                    }
                    taken[i] = true;
                    permutation.add(a[i]);
                    search();
                    taken[i] = false;
                    permutation.remove(permutation.size()-1);
                }
            }
        }
    }

    // generate subsets (call search and access subsets)
    public static class Subsets {
        List<List<Integer>> subsets = new ArrayList<>();
        List<Integer> subset = new ArrayList<>();

        void search(int[] a, int x) {
            if (x == a.length) {
                subsets.add(new ArrayList<>(subset));
            } else {
                subset.add(a[x]);
                search(a, x+1);
                subset.remove(subset.size() - 1);
                search(a, x+1);
            }
        }
    }

    public static int gcd(int a, int b) {
        while (b != 0) {
            int t = b;
            b = a % b;
            a = t;
        }
        return a;
    }

    public static int lcm(int a, int b) {
        return (a*b)/gcd(a, b);
    }

    public static int[] prefixSum(int[] a) {
        int n = a.length;
        int[] ps = new int[n];
        ps[0] = a[0];

        for (int i = 1; i<n; i++) {
            ps[i] = ps[i-1] + a[i];
        }

        return ps;
    }

    public static int[][] prefixSum2D(int[][] a) {
        int n = a.length;
        int m = a[0].length;
        int[][] ps = new int[n][m];
        ps[0][0] = a[0][0];

        for (int j = 1; j<m; j++) {
            ps[0][j] = ps[0][j-1] + a[0][j];
        }
        for (int i = 1; i<n; i++) {
            ps[i][0] = ps[i-1][0] + a[i][0];
        }

        for (int i = 1; i<n; i++) {
            for (int j = 1; j<m; j++) {
                ps[i][j] = ps[i-1][j] + ps[i][j-1] - ps[i-1][j-1] + a[i][j];
            }
        }

        return ps;
    }

    public static double log2(double a) {
        return log(a)/log(2);
    }

    //----------------------------------------DATA-STRUCTURES-----------------------------------------------------------

    // Range queries (i.e. RMQ) in O(1), others with functions in O(log n)
    public static class SparseTable {
        int[][] st;
        int n;
        int k;

        public SparseTable(int[] a) {
            n = a.length;
            k = (int) log2(n);
            st = new int[n][k+1];

            for (int i = 0; i<n; i++) {
                st[i][0] = a[i];
            }

            // 1<<j == 2^j
            for (int j = 1; j<=k; j++) {
                for (int i = 0; i + (1 << j) <= n; i++) {
                    st[i][j] = min(st[i][j-1], st[i + (1 << (j - 1))][j - 1]);
                }
            }
        }

        //not always available O(log n) -- change the constructor to use it
        public long sumQuery(int l, int r) {
            long sum = 0;
            for (int j = k; j>=0; j--) {
                if ((1 << j) <= r - l + 1) {
                    sum += st[l][j];
                    l += 1 << j;
                }
            }

            return sum;
        }

        //always available O(1) -- change this and the constructor for rangeMaxQuery
        public int rangeMinQuery(int l, int r) {
            int j = (int) log2(r - l + 1);
            int min = min(st[l][j], st[r - (1 << j) + 1][j]);
            return min;
        }

    }

    //Range Sum Dynamic Queries O(log n)
    public static class BinaryIndexedTree {

        int[] bit;

        public BinaryIndexedTree(int[] a) {
            int n = a.length;
            bit = new int[n+1];
            // Store the actual values in BITree[]
            // using update()
            for(int i = 0; i < n; i++)
                updateBit(i, a[i]);
        }

        // O(log n) update delta at index in the array (do it on the array and then call this function)
        public void updateBit(int index, int delta) {
            index += 1;

            while (index <= bit.length) {
                bit[index] += delta;

                index += index & (-index);
            }
        }

        // Computes sum a[0...index] in O(log n)
        public int getSum(int index) {
            int sum = 0;

            index += 1;

            while (index > 0) {
                sum += bit[index];

                index -= index & (-index);
            }

            return sum;
        }
    }

    public static class UnionFind {

        int[] link;
        int[] size;

        UnionFind(int n) {
            link = new int[n];
            size = new int[n];
            for (int i = 0; i<n; i++) {
                link[i] = i;
                size[i] = 1;
            }
        }

        int find(int x) {
            while (x != link[x]) x = link[x];
            return x;
        }

        boolean same(int a, int b) {
            return find(a) == find(b);
        }

        void unite(int a, int b) {
            a = find(a);
            b = find(b);

            if (size[a] < size[b]) {
                int temp = a;
                a = b;
                b = temp;
            }

            size[a] += size[b];
            link[b] = a;
        }
    }

    public static class SegmentTree {

        int st[];

        public SegmentTree(int arr[]) {
            int n = arr.length;

            int x = (int) (Math.ceil(log2(n)));

            int maxSize = 2 * (int) Math.pow(2, x) - 1;

            st = new int[maxSize];

            build(arr, 0, n-1, 0);
        }

        int build(int arr[], int ss, int se, int si) {
            if (ss == se) {
                st[si] = arr[ss];
                return arr[ss];
            }

            int mid = ss + (se - ss) / 2; //ss+se/2

            st[si] = build(arr, ss, mid, si * 2 + 1) +
                    build(arr, mid + 1, se, si * 2 + 2);
            return st[si];
        }

        private int getSumUtil(int ss, int se, int l, int r, int si) {
            if (l <= ss && r >= se) {
                return st[si];
            }

            if (se < l || ss > r) {
                return 0;
            }

            int mid = ss + (se - ss) / 2;
            return getSumUtil(ss, mid, l, r, 2 * si + 1) +
                    getSumUtil(mid + 1, se, l, r, 2 * si + 2);
        }

        void updateValueUtil(int ss, int se, int i, int diff, int si) {
            if (i < ss || i > se) {
                return;
            }

            st[si] = st[si] + diff;
            if (se != ss) {
                int mid = ss + (se - ss) / 2;
                updateValueUtil(ss, mid, i, diff, 2 * si + 1);
                updateValueUtil(mid + 1, se, i, diff, 2 * si + 2);
            }
        }

        int getSum(int n, int l, int r) {
            if (l < 0 || r > n - 1 || l > r) {
                return -1;
            }

            return getSumUtil(0, n-1, l, r, 0);
        }

        // don't do it directly on the array but use this function that will
        // do everything for you
        void updateValue(int arr[], int n, int i, int newValue) {
            if (i < 0 || i > n - 1) {
                return;
            }

            int diff = newValue - arr[i];

            arr[i] = newValue;

            updateValueUtil(0, n - 1, i, diff, 0);
        }
    }

    // Similar to Pair in c++, non-null objects as parameters
    public static class Pair<T extends Comparable<T>, Q extends Comparable<Q>> implements Comparable<Pair<T, Q>>{
        T a;
        Q b;

        public Pair(T a, Q b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair<?, ?> pair = (Pair<?, ?>) o;
            return a.equals(pair.a) && b.equals(pair.b);
        }

        @Override
        public int hashCode() {
            return Objects.hash(a, b);
        }


        @Override
        public int compareTo(Pair<T, Q> tqPair) {
            int compareA = this.a.compareTo(tqPair.a);

            if (compareA == 0) {
                return this.b.compareTo(tqPair.b);
            } else {
                return compareA;
            }
        }
    }


}