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 $(a_1+p_1,\ldots,a_N+p_N)$.

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.

Constraints

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

Sample Input 1

2
15 9

Sample Output 1

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.

Sample Input 2

5
1 2 3 10 10

Sample Output 2

No

Sample Input 3

4
1 1 1 1

Sample Output 3

Yes
0

All elements of A are equal from the beginning.

见题面 Input 部分

见题面 Output 部分