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 PYTHON3):

Solution:
#!/usr/bin/env python3
# set vim: fdm=marker sw=4 ts=4 et

from collections import defaultdict
from collections import deque

for _ in range(int(input())):
    n = int(input())
    a = [int(i) for i in input().split()]
    result = []
    for i in range(1, n):
        if a[i - 1] <= a[i]:
            if i == 1 or a[i - 2] == 1000000009:
                result.append((i, i + 1, 1000000007, a[i - 1]))
                a[i - 1], a[i] = (1000000007, a[i - 1])
            else:
                result.append((i, i + 1, 1000000009, a[i - 1]))
                a[i - 1], a[i] = (1000000009, a[i - 1])
        else:
            if i == 1 or a[i - 2] == 1000000009:
                result.append((i, i + 1, 1000000007, a[i]))
                a[i - 1] = 1000000007
            else:
                result.append((i, i + 1, 1000000009, a[i]))
                a[i - 1] = 1000000009
    print(len(result))
    for t in result:
        print(' '.join(map(str, t)))