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: Wrong Answer)

#![allow(unused_imports)]
use std::cmp::*;
use std::num::*;
use std::collections::*;
use itertools::Itertools;
use num::clamp;
use proconio::{input, marker::*, fastout};
use superslice::*;
#[allow(non_snake_case)]
#[allow(non_upper_case_globals)]
#[allow(non_camel_case_types)]
#[fastout()]
fn main(){
    input!{
        n:usize,
    }
    let mut k:usize=0;
    for i in 1..n{
        if i*(i+1)==2*n{
            k=i;
            break;
        }
    }
    if k==0{
        println!("No");
        return;
    }
    println!("Yes\n{}",k+1);
    let mut ans:Vec<Vec<i32>>=vec![Vec::new();k+1];
    let mut num=1;
    for i in 0..k+1{
        for j in 0..k-i{
            ans[i].push(num);
            num+=1;
        }
    }
    num=1;
    for i in 0..k+1{
        for j in i+1..k+1{
            ans[j].push(num);
            num+=1;
        }
    }
    for i in 0..k+1{
        print!("{} ",k);
        for j in 0..k{
            print!("{} ",ans[i][j]);
        }
        println!();
    }
}