Problem Statement

You are given a sequence of $N$ positive integers: $A = (A_1, A_2, \dots, A_N)$. Determine whether there is a pair of sequences $B = (B_1, B_2, \dots, B_x), C = (C_1, C_2, \dots, C_y)$ satisfying all of the conditions, and print one such pair if it exists.

• $1 ≤ x, y ≤ N$.
• $1 \le B_1 < B_2 < \dots < B_{x} \le N$.
• $1 \le C_1 < C_2 < \dots < C_{y} \le N$.
• $B$ and $C$ are different sequences.
• Here, we consider $B$ and $C$ different when $x ≠ y$ or there is an integer $i\ (1 ≤ i ≤ \min(x, y))$ such that $B_i ≠ C_i$.
• $A_{B_1} + A_{B_2} + \dots + A_{B_x}$ and $A_{C_1} + A_{C_2} + \dots + A_{C_y}$ are equal modulo $200$.

Constraints

• All values in input are integers.
• $2 \le N \le 200$
• $1 \le A_i \le 10^9$

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \dots A_N

Output

If there is no pair of sequences $B, C$ satisfying the conditions, print a single line containing No. Otherwise, print your choice of $B$ and $C$ in the following format:

Yes
x B_1 B_2 \dots B_x
y C_1 C_2 \dots C_y

The checker is case-insensitive: you can use either uppercase or lowercase letters.