Problem:
Score : 500 points

Problem Statement

You are given an integer N. Determine if there exists a tuple of subsets of \{1,2,...N\}, (S_1,S_2,...,S_k), that satisfies the following conditions:

Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.

Any two of the sets S_1,S_2,...,S_k have exactly one element in common.

If such a tuple exists, construct one such tuple.

Constraints

1 \leq N \leq 10^5

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

If a tuple of subsets of \{1,2,...N\} that satisfies the conditions does not exist, print No.
If such a tuple exists, print Yes first, then print such subsets in the following format:

k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}

where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.

If there are multiple such tuples, any of them will be accepted.

Sample Input 1

3

Sample Output 1

Yes
3
2 1 2
2 3 1
2 2 3

It can be seen that (S_1,S_2,S_3)=(\{1,2\},\{3,1\},\{2,3\}) satisfies the conditions.

Sample Input 2

4

Sample Output 2

No

Solution in Rust (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)]
use itertools::Itertools;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

fn tri(n: usize) -> Option<usize> {
    let n = 8 * n + 1;
    let r = (n as f64).sqrt() as usize;
    if r * r != n {
        return None;
    }
    Some((r as usize - 1) / 2)
}

fn main() {
    input! {
        n: usize,
    }

    if let Some(tri) = tri(n) {
        println!("Yes");
        let mut res = vec![vec![]; tri + 1];
        let mut a = 1;
        for i in 1..=tri {
            for j in 0..i {
                res[i].push(a);
                res[j].push(a);
                a += 1;
            }
        }
        println!("{}", tri + 1);
        for res in res {
            print!("{} ", res.len());
            for res in res {
                print!("{} ", res);
            }
            println!("");
        }
    } else {
        println!("No");
    }
}