B. Nastia and a Good Arraytime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputNastia has received an array of n positive integers as a gift.She calls such an array a good that for all i (2 \le i \le n) takes place gcd(a_{i - 1}, a_{i}) = 1, where gcd(u, v) denotes the greatest common divisor (GCD) of integers u and v.You can perform the operation: select two different indices i, j (1 \le i, j \le n, i \neq j) and two integers x, y (1 \le x, y \le 2 \cdot 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.InputThe first line contains a single integer t (1 \le t \le 10\,000) — the number of test cases.The first line of each test case contains a single integer n (1 \le n \le 10^5) — the length of the array.The second line of each test case contains n integers a_1, a_2, \ldots, a_{n} (1 \le a_i \le 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 \cdot 10^5.OutputFor each of t test cases print a single integer k (0 \le k \le 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 \le i \neq j \le n, 1 \le x, y \le 2 \cdot 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.ExampleInput
2
5
9 6 3 11 15
3
7 5 13
Output
2
1 5 11 9
2 5 7 6
0NoteConsider 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.
2
5
9 6 3 11 15
3
7 5 13

2 1 5 11 9 2 5 7 6 0
['constructive algorithms', 'math', 'number theory', '*1300']