Problem: Nastia has received an array of n positive integers as a gift.

She calls such an array a good that for all i (2 ≤ i ≤ n) takes place gcd(a_{i - 1}, a_{i}) = 1, where gcd(u, v) denotes the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers u and v.

You can perform the operation: select two different indices i, j (1 ≤ i, j ≤ n, i ≠ j) and two integers x, y (1 ≤ x, y ≤ 2 ⋅ 10^9) so that min{(a_i, a_j)} = min{(x, y)}. Then change a_i to x and a_j to y.

The girl asks you to make the array good using at most n operations.

It can be proven that this is always possible.

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains a single integer n (1 ≤ n ≤ 10^5) — the length of the array.

The second line of each test case contains n integers a_1, a_2, …, a_{n} (1 ≤ a_i ≤ 10^9) — the array which Nastia has received as a gift.

It's guaranteed that the sum of n in one test doesn't exceed 2 ⋅ 10^5.

Output

For each of t test cases print a single integer k (0 ≤ k ≤ n) — the number of operations. You don't need to minimize this number.

In each of the next k lines print 4 integers i, j, x, y (1 ≤ i ≠ j ≤ n, 1 ≤ x, y ≤ 2 ⋅ 10^9) so that min{(a_i, a_j)} = min{(x, y)} — in this manner you replace a_i with x and a_j with y.

If there are multiple answers, print any.

Example

Input


2
5
9 6 3 11 15
3
7 5 13


Output


2
1 5 11 9
2 5 7 6
0

Note

Consider the first test case.

Initially a = [9, 6, 3, 11, 15].

In the first operation replace a_1 with 11 and a_5 with 9. It's valid, because min{(a_1, a_5)} = min{(11, 9)} = 9.

After this a = [11, 6, 3, 11, 9].

In the second operation replace a_2 with 7 and a_5 with 6. It's valid, because min{(a_2, a_5)} = min{(7, 6)} = 6.

After this a = [11, 7, 3, 11, 6] — a good array.

In the second test case, the initial array is already good.

Solution (in JAVA):

Solution:

import java.util.*;

public class Example {
    static long[][] dp;
    //  static    int[]  ar;
    static int mod = 1000000000 + 7;
    static long[] ans = new long[100000 + 1];
    static List<List<Integer>> adj;
    static int[] vis;
    static int[] dis;
    static int row;
    static int col;
    static int[] arr;
    //  static  int n;
    static boolean tv;
    static List<Integer> list;
    static List<Integer> anslist;


    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        int[] nums={0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 29, 39, 49, 59, 69, 79, 89, 189, 289, 389, 489, 589, 689, 789, 1789, 2789, 3789, 4789, 5789, 6789, 16789, 26789, 36789, 46789, 56789, 156789, 256789, 356789, 456789, 1456789, 2456789, 3456789, 13456789, 23456789, 123456789};

        while (t > 0) {
            t--;
            int  n = sc.nextInt();
            int[] arr =new int[n];
            int min=Integer.MAX_VALUE;
             int ind=0;
            for(int i=0;i<n;i++){
                arr[i]=sc.nextInt();
                if(arr[i]<min){
                    min=arr[i];
                    ind=i;

                }
            }
            int k=n-1;
            int a=min+1;
            System.out.println(k);
            for(int i=ind-1;i>=0;i--){
                arr[i]=a;
                a++;




                }
            a=min+1;
            for(int i=ind+1;i<n;i++){
                arr[i]=a;
                a++;




            }
           // System.out.println(n-1);
            for(int i=0;i<n;i++){
                if(i!=ind){
                    System.out.println((i+1)+" "+((ind+1))+" " +arr[i]+" "+min);
                }
            }




          


        }
    }

    private static void allsunset(int i) {
        if (i == 10) {
            int sum = 0;
            for (Integer integer : list) {
                sum += integer;
            }
            // System.out.println(list.toString());
            // System.out.println(sum+" "+n);
            if (tv) {
                tv = true;
                Collections.sort(list);
                StringBuilder ans = new StringBuilder();
                for (int j = 0; j < list.size(); j++) {
                    ans.append(list.get(j));
                }
                System.out.println(ans);

            }

        } else {
            list.add(i);
            allsunset(i + 1);
            list.remove(list.size() - 1);
            allsunset(i + 1);
        }


    }


    private static boolean answer(int i, int k) {
        if (k == 0)
            return true;
        if (k < 0)
            return false;
        if (i <= 0)
            return false;
        return answer(i, k - arr[i]) || answer(i - 1, k);
    }


    private static long findans(int[] arr, int i, int s) {
        if (i < 0 && s == 0)
            return 0;
        if (i < 0 && s == 1)
            return 0;
        if (dp[i][s] != -1) {
            return dp[i][s];
        } else {


            if (s == 0)
                return dp[i][s] = Math.max(findans(arr, i - 1, s), -1 * arr[i] + findans(arr, i - 1, 1 - s));
            else
                return dp[i][s] = Math.max(findans(arr, i - 1, s), arr[i] + findans(arr, i - 1, 1 - s));
        }
    }

    public static void dfs(int v, int di) {
        dis[v] = di;
        vis[v] = 1;
        for (int i = 0; i < adj.get(v).size(); i++) {
            int x = adj.get(v).get(i);
            if (vis[x] == 0) {
                dfs(x, di + 1);
            }
        }
    }

    private static boolean isPrime(long a) {
        if (a == 1)
            return true;

        for (int i = 2; i * i <= a; i++) {
            if (a % i == 0)
                return false;

        }
        return true;
    }

    private static int gcd(int aa, int bb) {
        if (bb == 0)
            return aa;
        return gcd(bb, aa % bb);

    }

    private static int lowerBound(int[] ar, int a) {
        int res = 0;
        int s = 1;
        int e = ar.length - 1;
        while (s <= e) {
            int mid = (s) + (e - s) / 2;
            if (ar[mid] <= a) {
                res = mid;
                s = mid + 1;

            } else {
                e = mid - 1;
            }
        }
        return res;
    }

    public static int getXORSum(int[] arr1, int[] arr2) {

        long c = 0;
        int n = arr1.length;
        int m = arr2.length;
        if (n == 1 && m == 1) {
            return arr1[0] & arr2[0];
        }
        int aa = n + m;
        for (int i = 0; i < 32; i++) {

            int z = 0;
            int o = 0;
            int cc = 0;
            for (int a : arr1) {


                int x = (a & (1 << i));
                if (x == 0)
                    z++;
                else
                    o++;


            }
            for (int a : arr2) {
                int x = (a & (1 << i));
                if (x == 0)
                    z++;
                else
                    o++;
            }

            System.out.println(z + " " + o);

            if (z != aa && o != aa) {
                c = c + (1 << i);

            }


        }
        return (int) c;


    }


}