Description

Farmer John’s farm originally has $n$ barns. The $i$-th barn contains $a_i$ cows.

We define one operation of merging two barns $i, j$ ($a_i \ge a_j$) as follows: take $a_j$ cows out of barn $i$ and move them into barn $j$. If after the merge ends $a_i = 0$, then we can consider $a_i$ to have been merged, and the following operations will no longer be related to $a_i$.

Because time is running out, he decides to give you at most $1$ second.

Input Format

The first line contains an integer $T$, which denotes the number of test cases.

For the $t$-th test case:

Line $2t$ contains an integer $n$.

Line $2t + 1$ contains $n$ integers, where the $i$-th integer is $a_i$.

Output Format

For each test case:

If you find that it is impossible to reach the goal, output NO; otherwise output YES.

Then output one line containing an integer $m$, which denotes the number of operations.

Then output $m$ lines, each containing two numbers $i$ and $j$ (note that during an operation, it should satisfy $a_i \ge a_j$).

If there are multiple solutions, you may output any one of them.

3
4
1 2 3 2
5
3 9 6 18 12
5
2 3 5 7 11

YES
4
3 1
1 2
3 4
2 4
YES
6
2 1
1 2
4 3
2 3
4 5
3 5
NO

Hint

[Constraints and Notes]

For $100\%$ of the testdata, $1 \leq T \leq 5$, $1 \leq n \leq 10^5$, $0 \leq a_i \leq 10^9$.

Translated by ChatGPT 5