Score : $500$ points

Problem Statement

You are given a sequence of positive integers: $A=(a_1,\ldots,a_N)$.

Determine whether it is possible to make all elements of $A$ equal by repeating the following operation between $0$ and $10^4$ times, inclusive. If it is possible, show one way to do so.

• Choose a permutation $(p_1,\ldots,p_N)$ of $(1,\ldots,N)$, and replace $A$ with $(a_1+p_1,\ldots,a_N+p_N)$.

Constraints

• $2 \leq N \leq 50$
• $1 \leq a_i \leq 50$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$

$a_1$ $\ldots$ $a_N$

Output

If it is impossible to make all elements of $A$ equal, print No. If it is possible, print one way to do so in the following format, where $M$ is the number of operations, and $(p_{i,1},\ldots,p_{i,N})$ is the permutation chosen in the $i$-th operation:

Yes

$M$

$p_{1,1}$ $\ldots$ $p_{1,N}$

$\vdots$

$p_{M,1}$ $\ldots$ $p_{M,N}$

If multiple solutions exist, you may print any of them.

2
15 9

Yes
8
1 2
1 2
1 2
1 2
2 1
1 2
1 2
1 2

This sequence of $8$ operations makes $A = (24,24)$, where all elements are equal.

5
1 2 3 10 10

No

4
1 1 1 1

Yes
0

All elements of $A$ are equal from the beginning.