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 (1.15.1) (judge verdict: Wrong Answer)

#![allow(unused_parens)]
#![allow(unused_imports)]
#![allow(non_upper_case_globals)]
#![allow(non_snake_case)]
#![allow(unused_mut)]
#![allow(unused_variables)]
#![allow(dead_code)]

#[allow(unused_macros)]
macro_rules! invec {
    ( $ t : ty ) => {{
        let mut s = String::new();
        match std::io::stdin().read_line(&mut s) {
            Ok(0) => Vec::<$t>::new(),
            Ok(n) => s
                .trim()
                .split_whitespace()
                .map(|s| s.parse::<$t>().unwrap())
                .collect::<Vec<$t>>(),
            Err(_) => Vec::<$t>::new(),
        }
    }};
}

#[allow(unused_macros)]
macro_rules! get {
      ($t:ty) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              line.trim().parse::<$t>().unwrap()
          }
      };
      ($($t:ty),*) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              let mut iter = line.split_whitespace();
              (
                  $(iter.next().unwrap().parse::<$t>().unwrap(),)*
              )
          }
      };
      ($t:ty; $n:expr) => {
          (0..$n).map(|_|
              get!($t)
          ).collect::<Vec<_>>()
      };
      ($($t:ty),*; $n:expr) => {
          (0..$n).map(|_|
              get!($($t),*)
          ).collect::<Vec<_>>()
      };
      ($t:ty ;;) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              line.split_whitespace()
                  .map(|t| t.parse::<$t>().unwrap())
                  .collect::<Vec<_>>()
          }
      };
      ($t:ty ;; $n:expr) => {
          (0..$n).map(|_| get!($t ;;)).collect::<Vec<_>>()
      };
}

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [$t:tt]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
#[cfg(debug_assertions)]
macro_rules! mydbg {
    //($arg:expr) => (dbg!($arg))
    //($arg:expr) => (println!("{:?}",$arg));
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
      }
}
#[cfg(not(debug_assertions))]
macro_rules! mydbg {
    ($($arg:expr),*) => {};
}

macro_rules! echo {
    ($($a:expr),*) => {
          $(println!("{}",$a))*
      }
}

struct SliceDisplay<'a, T: 'a>(&'a [T]);
impl<'a, T: std::fmt::Display + 'a> std::fmt::Display for SliceDisplay<'a, T> {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        for item in self.0 {
            write!(f, "{} ", item)?;
        }
        Ok(())
    }
}

use std::cmp::*;
use std::collections::*;
use std::ops::{Add, Div, Mul, Sub};

#[allow(dead_code)]
static INF_I64: i64 = 92233720368547758;
#[allow(dead_code)]
static INF_I32: i32 = 21474836;
#[allow(dead_code)]
static INF_USIZE: usize = 18446744073709551;
#[allow(dead_code)]
static M_O_D: usize = 1000000007;
#[allow(dead_code)]
static PAI: f64 = 3.1415926535897932;

trait IteratorExt: Iterator {
    fn toVec(self) -> Vec<Self::Item>;
}

impl<T: Iterator> IteratorExt for T {
    fn toVec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

trait CharExt {
    fn toNum(&self) -> usize;
    fn toAlphabetIndex(&self) -> usize;
    fn toNumIndex(&self) -> usize;
}
impl CharExt for char {
    fn toNum(&self) -> usize {
        return *self as usize;
    }
    fn toAlphabetIndex(&self) -> usize {
        return self.toNum() - 'a' as usize;
    }
    fn toNumIndex(&self) -> usize {
        return self.toNum() - '0' as usize;
    }
}

trait VectorExt {
    fn joinToString(&self, s: &str) -> String;
}
impl<T: ToString> VectorExt for Vec<T> {
    fn joinToString(&self, s: &str) -> String {
        return self
            .iter()
            .map(|x| x.to_string())
            .collect::<Vec<_>>()
            .join(s);
    }
}

trait UsizeExt {
    fn pow(&self, n: usize) -> usize;
}
impl UsizeExt for usize {
    fn pow(&self, n: usize) -> usize {
        return ((*self as u64).pow(n as u32)) as usize;
    }
}

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

    let mut ans: usize = 0;
    let mut flag = false;
    let mut m = 0;
    for i in 1..n + 1 {
        mydbg!(i);
        if i * (i - 1) == n * 2 {
            flag = true;
            m = i;
            break;
        }
    }
    if !flag {
        echo!("No");
        return;
    }

    echo!("Yes");
    echo!(m);
    let mut map = vec![vec![0; m]; m];
    let mut c = 0;
    for i in 0..m {
        map[i][0] = m - 1;
        for j in 1..m {
            map[i][j] = c + 1;
            c = (c + 1) % m;
        }
        echo!(map[i].joinToString(" "));
    }
}