Nastia and a Good Array
Contest: Codeforces Round 720 (Div. 2)
Difficulty rating: 1300
Tags: constructive algorithms, math, number theory

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.

Input format:
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 $$$2 \cdot 10^5$$$.

Output format:
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.

Constraints:
Time limit: 2.0 s
Memory limit: 256.0 MB

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.

Example input:
2
5
9 6 3 11 15
3
7 5 13

Example output:
2
1 5 11 9
2 5 7 6
0

Editorial:
There are many ways to solve the problem. Here is one of them:
We will use the fact that $$$gcd(i, i + 1) = 1$$$ for any integer $$$i \ge 1$$$.
Let's find the minimum element $$$x$$$ of the array $$$a$$$ that is located in the position $$$pos$$$. Then for all integer $$$i$$$ ($$$1 \le i \le n$$$) perform the following operation: $$$(pos,\ i,\ x,\ x + abs(pos - i))$$$. That's how we replace $$$a_i$$$ to $$$x + abs(pos - i)$$$. The main condition: $$$\min{(a_i, a_j)} = \min{(x, y)}$$$ is satisfied because $$$a_{pos}$$$ always equals to $$$x$$$ and this value always less than any other element in the array $$$a$$$.
Consider the structure of the array $$$a$$$ after performing the operations describing above.
Let's define $$$l = x + pos - i$$$ and $$$r = x + i - pos$$$. These are the leftmost and the rightmost elements in the array $$$a$$$, respectively.
The array $$$a$$$ looks like $$$[l,\ l - 1\ \ldots\ x + 1,\ x,\ x + 1\ \ldots\ r - 1,\ r]$$$. Thus, we obtain an absolute difference, equal to one, between all pairs of adjacent elements.