A15499. Make Array Good

An array $b$ of $m$ positive integers is good if for all pairs $i$ and $j$ ( $1 \leq i,j \leq m$ ), $\max(b_i,b_j)$ is divisible by $\min(b_i,b_j)$ .

You are given an array $a$ of $n$ positive integers. You can perform the following operation:

- Select an index $i$ ( $1 \leq i \leq n$ ) and an integer $x$ ( $0 \leq x \leq a_i$ ) and add $x$ to $a_i$ , in other words, $a_i := a_i+x$ .
- After this operation, $a_i \leq 10^{18}$ should be satisfied.

You have to construct a sequence of at most $n$ operations that will make $a$ good. It can be proven that under the constraints of the problem, such a sequence of operations always exists.

Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 10^4$ ) — the number of test cases. The description of the test cases follows.

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

The second line of each test case contains $n$ space-separated integers $a_1,a_2,\ldots,a_n$ ( $1 \leq a_i \leq 10^9$ ) — representing the array $a$ .

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$ .

For each test, output a single integer $p$ ( $0 \leq p \leq n$ ) — denoting the number of operations in your solution.

In each of the following $p$ lines, output two space-separated integers — $i$ and $x$ .

You do not need to minimize the number of operations. It can be proven that a solution always exists.

In the first test case, array $a$ becomes $[5,5,5,5]$ after the operations. It is easy to see that $[5,5,5,5]$ is good.

In the second test case, array $a$ is already good.

In the third test case, after performing the operations, array $a$ becomes $[10,5,350,5,10]$ , which is good.

In the fourth test case, after performing the operations, array $a$ becomes $[60,10,20]$ , which is good.