# Peculiar Partitioning Anachor Replay of BUET Inter Univ...
Limits 1s, 1.0 GB

You are given an array $a$ of length $n$. You need to find a sub-sequence $S$ of the array such that $gcd(sum(S), sum(\overline S) )> 1.$ In other words, the gcd of sum of elements in $S$ and sum of elements not in $S$ is greater than 1. It is also required that both $S$ and $\overline S$ are non-empty.

## Input

The first line contains an integer, $n (2 \leq n \leq 10^6)$.

The second line contains $n$ space-separated integers $a_1, a_2, \cdots, a_n (1 \leq a_i \leq 2000)$.

## Output

If there is no sub-sequence of the array such that print a single word “No” .

Otherwise, on the first line print a single word “Yes” . On the second the line print a single integer $k \ (1 \leq k \leq n-1)$, the length of the chosen subsequence. On the third line print $k$ space seperated distinct integers $c_1, c_2, \cdots c_k\ (1 \leq c_i \leq n)$, the indices of the elements of the chosen subsequence.

If there are multiple solutions, print any of them. You can print the indices of the chosen subsequence in any order.

## Samples

InputOutput
5
6 2 3 5 8

Yes
3
4 2 3


Here $a_4, a_2, a_3$ are the chosen elements. Their sum is $5+2+3=10$. The other elements sum to $6+8=14$. Since, $gcd(10, 14) > 1$, this is a valid answer.

$[1 , 5]$, $[3, 4]$ , $[1, 2, 5, 4]$ are also valid subsequences.

InputOutput
2
1 3

No


Given a sub-sequence $S$ of an array $a$, $\overline S$ is the sub-sequence formed by taking all elements in $a$ and not in $S$. For example, given an array $a = [10, 20, 30, 40, 50]$ and the subsequence $S = [20, 30, 50]$, then $\overline S = [10, 40]$.

### Submit 