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, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};
fn main() {
    input! {//
        n:i64,
    }
    let mut st = BTreeSet::new();
    let mut c = 0;
    for i in 1i64.. {
        let k = i * (i + 1) / 2;
        if k > 111111 {
            break;
        }
        st.insert(k);
        if k == n {
            c = i;
        }
    }

    if !st.contains(&n) {
        yn(false);
        return;
    } else {
        yn(true);
    }
    println!("{}", c + 1);
    let mut c = c as usize;
    let mut ans = vec![vec![]; c + 1];

    let mut sum = 1;
    for k in (1..=c).rev() {
        for i in 0..k {
            ans[c - k].push(sum + i);
            ans[c + i + 1 - k].push(sum + i);
        }
        sum += k;
    }

    for v in ans.iter() {
        print!("{} ", c);
        for &x in v.clone().iter() {
            print!("{} ", x);
        }
        println!("");
    }
}
pub fn yn(ans: bool) {
    if ans {
        println!("Yes");
    } else {
        println!("No");
    }
}