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 C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.InteropServices;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using static Math2;
using static io;
using static Utils;

public class CompetitiveProgramming {
  public void Solve () {
    var ok = new Tuple<bool, int>[100001];
    for (int i = 1; i * (i + 1) / 2 <= 100000; ++i) ok[i * (i + 1) / 2] = new Tuple<bool, int> (true, i);
    var N = Int1;
    if (!ok[N].Item1) {
      Put ("No");
      return;
    }
    var x = ok[N].Item2;
    var ans = new int[x + 1][];
    int tot = 0;
    for (int i = 0; i < x + 1; ++i) {
      ans[i] = new int[x];
      for (int j = i; j < x; ++j) {
        ans[i][j] = ++tot;
      }
    }
    tot = 0;
    for (int i = 0; i < x; ++i) {
      for (int j = i + 1; j < x + 1; ++j) {
        ans[j][i] = ++tot;
      }
    }
    Put (x + 1);
    for (int i = 0; i < x + 1; ++i) Put (x + " " + string.Join (" ", ans[i]));

  }
}

public static class NumberTheory {
  public static Dictionary<long, int> PrimeFactorization (long N) {
    var ret = new Dictionary<long, int> ();
    for (long i = 2; i * i <= N; ++i) {
      int cnt = 0;
      while (N % i == 0) {
        cnt++;
        N /= i;
      }
      if (cnt != 0) ret[i] = cnt;
    }
    if (N >= 2) ret[N] = 1;
    return ret;
  }
  public static Dictionary<int, int> FactoricalPF (int N) {
    var ret = new Dictionary<int, int> ();
    for (int i = 2; i <= N; ++i) {
      int ni = i;
      for (int j = 2; j * j <= ni; ++j) {
        int cnt = 0;
        while (ni % j == 0) {
          ++cnt;
          ni /= j;
        }
        if (cnt == 0) continue;
        if (ret.ContainsKey (j))
          ret[j] += cnt;
        else ret[j] = cnt;
      }
      if (ni >= 2) {
        if (ret.ContainsKey (ni))
          ret[ni] += 1;
        else ret[ni] = 1;
      }
    }
    return ret;
  }
  public static List<long> DivisorEnumrate (long N) {
    var ret = new List<long> ();
    for (long i = 1; i * i <= N; ++i) {
      if (N % i == 0) {
        ret.Add (i);
        ret.Add (N / i);
      }
    }
    return ret;
  }
  public static List<int> seive (int n) {
    var ret = new List<int> ();
    bool[] isPrime = new bool[n + 1];
    for (int i = 1; i <= n; ++i) isPrime[i] = true;
    isPrime[1] = false;
    for (int i = 1; i <= n; ++i) {
      int j = i;
      if (isPrime[i]) ret.Add (i);
      else continue;
      while (j <= n) {
        j += i;
        if (j > n) continue;
        isPrime[j] = false;
      }
    }
    return ret;
  }
  public static bool isPrime (long n) {
    for (int i = 2; i * i <= n; ++i) {
      if (n % i == 0) return false;
    }
    return true;
  }
}

public class BinarySearch {
  public static int Lower_Bound<T> (IList<T> list, T Target) => Lower_Bound<T> (list, Target, Comparer<T>.Default.Compare);
  public static int Lower_Bound<T> (IList<T> list, T Target, Comparison<T> Comp) {
    var cmp = Comparer<T>.Create (Comp);
    var l = -1; //always ng
    var r = list.Count (); //always ok
    while (r - l > 1) {
      var mid = l + (r - l) / 2;
      var res = cmp.Compare (list[mid], Target);
      if (res >= 0) r = mid;
      else l = mid;
    }
    return r;
  }
  public static int Upper_Bound<T> (IList<T> list, T Target) => Upper_Bound<T> (list, Target, Comparer<T>.Default.Compare);
  public static int Upper_Bound<T> (IList<T> list, T Target, Comparison<T> Comp) {
    var cmp = Comparer<T>.Create (Comp);
    var l = -1;
    var r = list.Count;
    while (r - l > 1) {
      var mid = l + (r - l) / 2;
      var res = cmp.Compare (list[mid], Target);
      if (res > 0) r = mid;
      else l = mid;
    }
    return r;
  }
}

public static class Math2 {
  public const int INF = 1 << 29;
  public const long INFL = 1L << 60;
  public const long MOD = 1000000007;
  public const int MOD2 = 998244353;

  public static long Power (long a, long b, long MOD = 1000000007) //i^N
  {
    long res = 1;
    while (b > 0) {
      if ((b & 1) != 0) res = res * a % MOD;
      a = a * a % MOD;
      b >>= 1;
    }
    return res;
  }
  public static long Power2 (long a, long b) //i^N
  {
    long res = 1;
    while (b > 0) {
      if ((b & 1) != 0) res = res * a;
      a = a * a;
      b >>= 1;
    }
    return res;
  }
  public static long GCD (long a, long b) {
    while (b > 0) {
      var r = a % b;
      a = b;
      b = r;
    }
    return a;
  }
  public static long LCM (long a, long b) => (b / GCD (a, b)) * a;
  public static long Comb (long n, long r, int MOD = 1000000007) {
    if (r > n - r) r = n - r;
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i) {
      Deno = (Deno * i) % MOD;
      Nume = Nume * (n - i + 1) % MOD;
    }
    return (Nume * inv (Deno)) % MOD;
  }
  public static long Comb2 (long n, long r) {
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i) {
      Deno *= i;
      Nume *= n - i + 1;
    }
    return Nume / Deno;
  }
  public static long inv (long x, int MOD = 1000000007) {
    return Power (x, MOD - 2, MOD);
  }
}
public static class Utils {
  public static void Swap<T> (ref T A, ref T B) {
    T x = A;
    A = B;
    B = x;
  }
  public static int DigitSum (int N) {
    string s = N.ToString ();
    int ret = 0;
    for (int i = 0; i < s.Length; ++i) ret += s[i] - '0';
    return ret;
  }
  public static string ConvertBase (long N, int K) {
    StringBuilder ret = new StringBuilder ();
    while (N > 0) {
      var r = N % K;
      N /= K;
      ret.Append (r);
    }
    return new string (ret.ToString ().ToCharArray ().Reverse ().ToArray ());
  }
}
class Program {
  static void Main (string[] args) {
    var CompetitiveProgramming = new CompetitiveProgramming ();
    CompetitiveProgramming.Solve ();
  }
}
public static class io {
  public static string Str => Console.ReadLine ();
  public static string[] Strs => Str.Split (' ');
  public static long[] Longs => Strs.Select (long.Parse).ToArray ();
  public static int[] Ints => Strs.Select (int.Parse).ToArray ();
  public static char[] Chars => Str.ToArray ();
  public static double[] Doubles => Strs.Select (double.Parse).ToArray ();
  public static long Long1 => Longs[0];
  public static int Int1 => Ints[0];
  public static char Char1 => Chars[0];
  public static double Double1 => Doubles[0];
  public static long[] VerticalRead (int N) { long[] A = new long[N]; for (int i = 0; i < N; ++i) A[i] = Long1; return A; }
  public static void Put (string a) => Console.WriteLine (a);
  public static void Put (params object[] i) => Put (string.Join (" ", i));
  public static void Put<T> (IEnumerable<T> a) => Put (string.Join (" ", a));
  public static void VerticalPut<T> (IEnumerable<T> a) { foreach (var z in a) Put (z); }
  public static void YN (bool i) {
    if (i) Put ("Yes");
    else Put ("No");
  }
}