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.*;
import java.lang.*;

public class Main {
    //input
    static out op = new out();
    static inp ip = new inp();
    static FastReader sc = new FastReader();
    static BufferedWriter output = new BufferedWriter( 
        new OutputStreamWriter(System.out));
    static long inf = (long)1e18+7;
   
   static long mod = (long)1e9+7;
   static long z = 0;

   static void sol() throws Exception{
      int n = ip.in();
      int[] arr = new int[n];
      PriorityQueue<Node> pq = new PriorityQueue<>();
      for(int i=0;i<n;i++){
         arr[i] = ip.in();
         pq.add(new Node(arr[i],i));
      }
      
      int k = 0;
      StringBuffer sb = new StringBuffer();
      
      while(pq.size()>1){
         int a = pq.peek().data;
         int ai = pq.remove().ind;

         int bi = pq.peek().ind;
         int b = pq.remove().data;
         
         pq.add(new Node(a-b,ai));
         op.sbln(a+" "+b);
         if(b == 0)break;
         while(b>0){
            sb.append((ai+1)+" "+(bi+1)+"\n");
            b--;
            k++;
         }
      }
      op.sbln(k);
      op.sb(sb+"");
   }
   
   
   static long gcd(long a,long b){
     if(b==0)
     return a;
     return gcd(b,a%b);
   }
   
   public static void main(String[] args) throws Exception { 
       
      int t = ip.in();
      while(t-- > 0){
          sol();
      }
      op.output.flush();
    }
    static class Node implements Comparable<Node>{
       int data;
       int ind;
      //  Node left,right;
      //  Node(){
      //       left = null;
      //       right = null;
      //  }
       Node(int data,int ind){
            this.data = data;
            this.ind = ind;
       }
    
         @Override
         public int compareTo(Node o) {
             if(this.data == o.data)
             return o.ind - this.ind;
             // TODO Auto-generated method stub
             return o.data - this.data;
         }
    }
}


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; 
    }

}
class inp{
    FastReader sc = new FastReader();
    int in(){
        int a = sc.nextInt();
        return a;
    }
    long lin(){
        long a = sc.nextLong();
        return a;
    }
    char cin(){
        char c = sc.next().charAt(0);
        return c;
    }
    char[] cain(){
        char[] a = sc.nextLine().toCharArray();
        return a;
    }
    int[] arrin(int n){
        int [] arr = new int[n];
        for(int i=0;i<n;i++)
            arr[i] = in();

        return arr;
    }
    int[] mm_arr(int[] arr){
        int max = Integer.MIN_VALUE;
        int min = Integer.MAX_VALUE;
        for(int i=0;i<arr.length;i++){
            max = Math.max(max,arr[i]);
            min = Math.min(min,arr[i]);
        }
        int ans[] = {max,min};
        return ans;
    }
    int[] srt(int[] arr){
        Arrays.sort(arr);
        return arr;
    }
    long pow(long a,long b){
        if(b == 0)return 1;
        long res = pow(a,b/2);
        //System.out.println(res + " " + b + " " + (b&1));
        if((b&1) == 0)return res*res;
        return a*res*res; 
    }

   //  boolean[] prime(){
   //     boolean prime[] = new boolean[100000001];
   //     Arrays.fill(prime,true);
   //     for (int p = 2; p * p <= 10000000; p++)
   //     {
   //          // If prime[p] is not changed,
   //          // then it is a prime
   //          if (prime[p] == true)
   //          {
   //              // Update all multiples
   //              // of p greater than or
   //              // equal to the square of it
   //              // numbers which are multiple
   //              // of p and are less than p^2
   //              // are already been marked.
   //              for (int i = p * p; i <= 10000000; i += p)
   //                 prime[i] = false;
   //          }
   //     }
   //     return prime;
   //  }
}
class out{
    BufferedWriter output = new BufferedWriter( 
        new OutputStreamWriter(System.out)); 

    void sb(String s) throws IOException {
        output.write(s);
    }
    void sbln(Object s) throws IOException {
        output.write(s+"\n");
    }
    void yes() throws IOException{
        output.write("YES\n");
    }
    void no() throws IOException{
        output.write("NO\n");
    }
}