There are $n$ soda sitting around a round table. soda are numbered from $1$ to $n$ and $i$-th soda is adjacent to $(i+1)$-th soda, $1$-st soda is adjacent to $n$-th soda.
Each soda has some candies in their hand. And they want to make the number of candies the same by doing some taking and giving operations. More specifically, every two adjacent soda $x$ and $y$ can do one of the following operations only once:
1. $x$-th soda gives $y$-th soda a candy if he has one;
2. $y$-th soda gives $x$-th soda a candy if he has one;
3. they just do nothing.
Now you are to determine whether it is possible and give a sequence of operations.
There are multiple test cases. The first line of input contains an integer $T$, indicating the number of test cases. For each test case:
The first contains an integer $n$ $(1 \le n \le 10^5)$, the number of soda.
The next line contains $n$ integers $a_1, a_2, \dots, a_n$ $(0 \le a_i \le 10^9)$, where $a_i$ denotes the candy $i$-th soda has.
For each test case, output "YES" (without the quotes) if possible, otherwise output "NO" (without the quotes) in the first line. If possible, then the output an integer $m$ $(0 \le m \le n)$ in the second line denoting the number of operations needed. Then each of the following $m$ lines contain two integers $x$ and $y$ $(1 \le x, y \le n)$, which means that $x$-th soda gives $y$-th soda a candy.