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.