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.util.Collections;
import java.util.HashSet;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;
public class C{
// author: Tarun Verma
	static FastScanner sc = new FastScanner();
	static int inf = Integer.MAX_VALUE;
	static long mod = 1000000007;
	
	/* Common Mistakes By Me
	 * make sure to read the bottom part of question
	 * special cases (n=1?)
	 * In Game Theory Check your solution and consider all the solutions
	 * Always initialise value to the declare array in local scope
	 * don't use debugs in interactive problems
	 * Always Reset vis,adj array upto n+1 otherwise can cause TLE
	 */
	public static void solve() {
		int n = sc.nextInt();
		int a[] = sc.readArray(n);
		HashSet<pair> st = new HashSet<pair>();
		for(int i =0;i<n;i++) {
	        if(a[i] == 0) continue;
	        st.add(new pair(a[i],i+1));
	    }
		ArrayList<pair> ans = new ArrayList<pair>();
		while((st.size()) > 1) {
	        pair P1 = new pair();
	        for(pair i: st) {
	        	P1 = i;
	        	break;
	        }
	        pair P2 = new pair( );
	        for(pair i: st) {
	        	P2 = i;
	        }
//	        System.out.println(P1.sc+ " " +P2.sc);
	        ans.add(new pair(P1.sc,P2.sc));
//	        for(pair ii: ans) {
//	        	System.out.println(ii.fr + " " + ii.sc);
//	        }
	        st.remove(P1);
	        st.remove(P2);
	        if(P1.fr-1 > 0) {
	            st.add(new pair(P1.fr-1,P1.sc));
	        }
	        if(P2.fr-1 > 0) {
	        	st.add(new pair(P2.fr-1,P2.sc));
	        }
	    }
		System.out.println(ans.size());
		for(pair i: ans) {
			System.out.println(i.fr + " " + i.sc);
		}
	}
	
	public static void main(String[] args) {
		int t = 1;
		t = sc.nextInt();
		outer: for (int tt = 0; tt < t; tt++) {
			solve();
		}
	}
	
////////////////////////////////////////////////////////////////////////////////////
////////////////////DO NOT BELOW BEFORE THIS LINE //////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////
	
	static boolean isPalindrom(char[] arr, int i, int j) {
		boolean ok = true;
		while (i <= j) {
			if (arr[i] != arr[j]) {
				ok = false;
				break;
			}
			i++;
			j--;
		}
		return ok;
	}
	
	static int max(int a, int b) {
		return Math.max(a, b);
	}
	
	static int min(int a, int b) {
		return Math.min(a, b);
	}
	
	static long max(long a, long b) {
		return Math.max(a, b);
	}
	
	static long min(long a, long b) {
		return Math.min(a, b);
	}
	static void sort(int arr[]) {
		ArrayList<Integer> a = new ArrayList<Integer>();
		for(int i: arr) a.add(i);
		Collections.sort(a);
		for(int i=0;i<arr.length;i++) arr[i] = a.get(i);
	}
	static void sort(long arr[]) {
		ArrayList<Long> a = new ArrayList<Long>();
		for(long i: arr) a.add(i);
		Collections.sort(a);
		for(int i=0;i<arr.length;i++) arr[i] = a.get(i);
	}
	static int abs(int a) {
		return Math.abs(a);
	}
	
	static long abs(long a) {
		return Math.abs(a);
	}
	
	static void swap(long arr[], int i, int j) {
		long temp = arr[i];
		arr[i] = arr[j];
		arr[j] = temp;
	}
	
	static void swap(int arr[], int i, int j) {
		int temp = arr[i];
		arr[i] = arr[j];
		arr[j] = temp;
	}
	
	static int maxArr(int arr[]) {
		int maxi = Integer.MIN_VALUE;
		for (int x : arr)
			maxi = max(maxi, x);
		return maxi;
	}
	
	static int minArr(int arr[]) {
		int mini = Integer.MAX_VALUE;
		for (int x : arr)
			mini = min(mini, x);
		return mini;
	}
	
	static long maxArr(long arr[]) {
		long maxi = Long.MIN_VALUE;
		for (long x : arr)
			maxi = max(maxi, x);
		return maxi;
	}
	
	static long minArr(long arr[]) {
		long mini = Long.MAX_VALUE;
		for (long x : arr)
			mini = min(mini, x);
		return mini;
	}
	
	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 void ruffleSort(int[] a) {
		int n = a.length;
		Random r = new Random();
		for (int i = 0; i < a.length; i++) {
			int oi = r.nextInt(n);
			int temp = a[i];
			a[i] = a[oi];
			a[oi] = temp;
		}
		Arrays.sort(a);
	}
	
	public static int binarySearch(int a[], int target) {
		int left = 0;
		int right = a.length - 1;
		int mid = (left + right) / 2;
		int i = 0;
		while (left <= right) {
			if (a[mid] <= target) {
				i = mid + 1;
				left = mid + 1;
			} else {
				right = mid - 1;
			}
			mid = (left + right) / 2;
		}
		return i;
	}
	
	static class FastScanner {
		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();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		int[] readArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
		
		long[] readLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}
		
		int[][] read2dArray(int n, int m) {
			int arr[][] = new int[n][m];
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < m; j++) {
					arr[i][j] = nextInt();
				}
			}
			return arr;
		}
		
		ArrayList<Integer> readArrayList(int n) {
			ArrayList<Integer> arr = new ArrayList<Integer>();
			for (int i = 0; i < n; i++) {
				int a = nextInt();
				arr.add(a);
			}
			return arr;
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
	}
	
	static class pair {
		int fr, sc;
		pair(){}
		pair(int fr, int sc) {
			this.fr = fr;
			this.sc = sc;
		}
	}
	
////////////////////////////////////////////////////////////////////////////////////	
	
}
