3-Second Sort

While you are peacefully reading this problem, the extremist fundamentalist mint-chocolate terrorist Kim Junwon has already seized the school outside the auditorium.

If you do not make the given sequence sorted in ascending order within 3 seconds, the mint-chocolate bomb planted in the auditorium will explode.

You may replace any element $A_i$ of the sequence with another number $X$.

This operation takes 1 second.

3...

2...

1...

The first line gives the length $N$ of the sequence you must make sorted.

The second line gives $N$ integers $A_1, A_2, \cdots , A_N$ representing the elements of the sequence, separated by spaces.

If you can make the sequence sorted in ascending order within 3 operations,

• Print YES on the first line.

• From the second line onward, print a method to make the sequence sorted in the following form.

  • On the first line, print the number of operations $K$.
  • Then, over $K$ lines, print the operations to apply in order.
    Specifically, on each line print two integers $i$ and $X$. This means the operation of replacing element $A_i$ with $X$. ($1 \le i \le N$, $1 \leq X \leq 1\,000\,000\,000$)

You do not need to minimize the number of operations, and if several methods are possible, you may print any one of them. You may modify the same element multiple times.

If you cannot make the sequence sorted in ascending order within 3 operations,

• Print NO on the first line.

• $1 \leq N \leq 200\,000$
• $1 \leq A_i \leq 1\,000\,000\,000$ ($1 \le i \le N$)
• The sequence is not given already sorted in ascending order.

A sequence $A_1, \cdots, A_N$ being sorted in ascending order means that $A_1 \le A_2$, $A_2 \le A_3$, $\cdots$, $A_{N-1} \le A_N$.