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.util.*;
import java.io.*;


public class Main {
	static StringBuilder sb;
	static dsu dsu;
	static long fact[];
	static int mod = (int) (1e9 + 7);

	static void solve() {
	    StringBuilder sb1=new StringBuilder();
		int n=i();
		int[] arr=new int[n];
		for(int i=0;i<n;i++)arr[i]=i();
		PriorityQueue<Pair> pq=new PriorityQueue<>();
		for(int i=0;i<n;i++){
		    if(arr[i]!=0){
		    pq.add(new Pair(i,arr[i]));}
		}
		int t=0;
		while(pq.size()>1){
		   Pair p1=pq.remove();
		   Pair p2=pq.remove();
		   int v1=p1.val;
		   int v2=p2.val;
		   int min=Math.min(v1,v2);
		   t+=min;
		   for(int i=1;i<=min;i++){
		       sb1.append((p1.idx+1)+" "+(p2.idx+1)+"\n");
		   }
		   p1.val-=min;
		   p2.val-=min;
		   if(p1.val!=0)pq.add(p1);
		   if(p2.val!=0)pq.add(p2);
		   
		   
		   
		   
		    
		    
		}
		sb.append(t+"\n");
		sb.append(sb1);
		
		
	}

	public static void main(String[] args) {
		sb = new StringBuilder();
		int test = i();
		while (test-- > 0) {
			solve();
		}
		System.out.println(sb);

	}

	/*
	 * fact=new long[(int)1e6+10]; fact[0]=fact[1]=1; for(int i=2;i<fact.length;i++)
	 * { fact[i]=((long)(i%mod)1L(long)(fact[i-1]%mod))%mod; }
	 */
//**************NCR%P******************	 
	static long ncr(int n, int r) {
		if (r > n)
			return (long) 0;

		long res = fact[n] % mod;
		// System.out.println(res);
		res = ((long) (res % mod) * (long) (p(fact[r], mod - 2) % mod)) % mod;
		res = ((long) (res % mod) * (long) (p(fact[n - r], mod - 2) % mod)) % mod;
		// System.out.println(res);
		return res;

	}

	static long p(long x, long y)// POWER FXN //
	{
		if (y == 0)
			return 1;

		long res = 1;
		while (y > 0) {
			if (y % 2 == 1) {
				res = (res * x) % mod;
				y--;
			}

			x = (x * x) % mod;
			y = y / 2;

		}
		return res;
	}

//**************END******************

	// *************Disjoint set
	// union*********//
	static class dsu {
		int parent[];

		dsu(int n) {
			parent = new int[n];
			for (int i = 0; i < n; i++)
				parent[i] = -1;
		}

		int find(int a) {
			if (parent[a] < 0)
				return a;
			else {
				int x = find(parent[a]);
				parent[a] = x;
				return x;
			}
		}

		void merge(int a, int b) {
			a = find(a);
			b = find(b);
			if (a == b)
				return;
			parent[b] = a;
		}
	}

//**************PRIME FACTORIZE **********************************//
	static TreeMap<Integer, Integer> prime(long n) {
		TreeMap<Integer, Integer> h = new TreeMap<>();
		long num = n;
		for (int i = 2; i <= Math.sqrt(num); i++) {
			if (n % i == 0) {
				int nt = 0;
				while (n % i == 0) {
					n = n / i;
					nt++;
				}
				h.put(i, nt);
			}
		}
		if (n != 1)
			h.put((int) n, 1);
		return h;

	}

//****CLASS PAIR ************************************************
	static class Pair implements Comparable<Pair> {
		int idx;
		int val;

		Pair(int idx, int val) {
			this.idx = idx;
			this.val = val;
		}

		public int compareTo(Pair o) {
			return (int) (o.val - this.val);

		}

	}
//****CLASS PAIR **************************************************

	static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;

		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 int Int() {
			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 String String() {
			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 String();
		}

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

	static class OutputWriter {
		private final PrintWriter writer;

		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}

		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}

		public void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}

		public void printLine(Object... objects) {
			print(objects);
			writer.println();
		}

		public void close() {
			writer.close();
		}

		public void flush() {
			writer.flush();
		}
	}

	static InputReader in = new InputReader(System.in);
	static OutputWriter out = new OutputWriter(System.out);

	public static long[] sort(long[] a2) {
		int n = a2.length;
		ArrayList<Long> l = new ArrayList<>();
		for (long i : a2)
			l.add(i);
		Collections.sort(l);
		for (int i = 0; i < l.size(); i++)
			a2[i] = l.get(i);
		return a2;
	}

	public static char[] sort(char[] a2) {
		int n = a2.length;
		ArrayList<Character> l = new ArrayList<>();
		for (char i : a2)
			l.add(i);
		Collections.sort(l);
		for (int i = 0; i < l.size(); i++)
			a2[i] = l.get(i);
		return a2;
	}

	public static long pow(long x, long y) {
		long res = 1;
		while (y > 0) {
			if (y % 2 != 0) {
				res = (res * x);// % modulus;
				y--;

			}
			x = (x * x);// % modulus;
			y = y / 2;
		}
		return res;
	}

//GCD___+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
	public static long gcd(long x, long y) {
		if (x == 0)
			return y;
		else
			return gcd(y % x, x);
	}
	// ******LOWEST COMMON MULTIPLE
	// *********************************************

	public static long lcm(long x, long y) {
		return (x * (y / gcd(x, y)));
	}

//INPUT PATTERN********************************************************
	public static int i() {
		return in.Int();
	}

	public static long l() {
		String s = in.String();
		return Long.parseLong(s);
	}

	public static String s() {
		return in.String();
	}

	public static int[] readArrayi(int n) {
		int A[] = new int[n];
		for (int i = 0; i < n; i++) {
			A[i] = i();
		}
		return A;
	}

	public static long[] readArray(long n) {
		long A[] = new long[(int) n];
		for (int i = 0; i < n; i++) {
			A[i] = l();
		}
		return A;
	}

}