CF1521B.Nastia and a Good Array

Nastia 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.

The 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 $2 \cdot 10^5$ .

For 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.

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.