Problem:
Score : 300 points

Problem Statement

The problem set at CODE FESTIVAL 20XX Finals consists of N problems.

The score allocated to the i-th (1≦i≦N) problem is i points.

Takahashi, a contestant, is trying to score exactly N points. For that, he is deciding which problems to solve.

As problems with higher scores are harder, he wants to minimize the highest score of a problem among the ones solved by him.

Determine the set of problems that should be solved.

Constraints

1≦N≦10^7

Partial Score

200 points will be awarded for passing the test set satisfying 1≦N≦1000.

Additional 100 points will be awarded for passing the test set without additional constraints.

Input

The input is given from Standard Input in the following format:

N

Output

Among the sets of problems with the total score of N, find a set in which the highest score of a problem is minimum, then print the indices of the problems in the set in any order, one per line.

If there exists more than one such set, any of them will be accepted.

Sample Input 1

4

Sample Output 1

1
3

Solving only the 4-th problem will also result in the total score of 4 points, but solving the 1-st and 3-rd problems will lower the highest score of a solved problem.

Sample Input 2

7

Sample Output 2

1
2
4

The set \{3,4\} will also be accepted.

Sample Input 3

1

Sample Output 3

1

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;
using System.IO;

using static util;
using P = pair<int, int>;

using Binary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.ParameterExpression,
                           System.Linq.Expressions.BinaryExpression>;
using Unary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.UnaryExpression>;

class Program
{
    static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    static Scan sc = new Scan();
    const int M = 1000000007;
    const int M2 = 998244353;
    const long LM = (long)1e18;
    const double eps = 1e-11;
    static readonly int[] dd = { 0, 1, 0, -1, 0 };
    const string dstring = "RDLU";
    static void Main()
    {
        int n = sc.Int;
        for (int i = 1; i <= n; i++)
        {
            if (i * (i + 1) / 2 >= n) {
                int rem = i * (i + 1) / 2 - n;
                for (int j = 1; j <= i; j++)
                {
                    if (j != rem) Prt(j);
                }
                break;
            }
        }
        sw.Flush();
    }

    static void DBG(string a) => Console.WriteLine(a);
    static void DBG<T>(IEnumerable<T> a) => DBG(string.Join(" ", a));
    static void DBG(params object[] a) => DBG(string.Join(" ", a));
    static void Prt(string a) => sw.WriteLine(a);
    static void Prt<T>(IEnumerable<T> a) => Prt(string.Join(" ", a));
    static void Prt(params object[] a) => Prt(string.Join(" ", a));
}
class pair<T, U> : IComparable<pair<T, U>>
{
    public T v1;
    public U v2;
    public pair(T v1, U v2) {
        this.v1 = v1;
        this.v2 = v2;
    }
    public int CompareTo(pair<T, U> a) {
        int c = Comparer<T>.Default.Compare(v1, a.v1);
        return c != 0 ? c : Comparer<U>.Default.Compare(v2, a.v2);
    }
    public override string ToString() => v1 + " " + v2;
    public void Deconstruct(out T a, out U b) {
        a = v1; b = v2;
    }
}
static class util
{
    public static pair<T, T> make_pair<T>(this IList<T> l) => make_pair(l[0], l[1]);
    public static pair<T, U> make_pair<T, U>(T v1, U v2) => new pair<T, U>(v1, v2);
    public static T sq<T>(T a) => Operator<T>.Multiply(a, a);
    public static T Max<T>(params T[] a) => a.Max();
    public static T Min<T>(params T[] a) => a.Min();
    public static bool inside(int i, int j, int h, int w) => i >= 0 && i < h && j >= 0 && j < w;
    public static void swap<T>(ref T a, ref T b) where T : struct { var t = a; a = b; b = t; }
    public static void swap<T>(this IList<T> a, int i, int j) where T : struct { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a) {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
static class Operator<T>
{
    static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x");
    static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y");
    public static readonly Func<T, T, T> Add = Lambda(Expression.Add);
    public static readonly Func<T, T, T> Subtract = Lambda(Expression.Subtract);
    public static readonly Func<T, T, T> Multiply = Lambda(Expression.Multiply);
    public static readonly Func<T, T, T> Divide = Lambda(Expression.Divide);
    public static readonly Func<T, T> Plus = Lambda(Expression.UnaryPlus);
    public static readonly Func<T, T> Negate = Lambda(Expression.Negate);
    public static Func<T, T, T> Lambda(Binary op) => Expression.Lambda<Func<T, T, T>>(op(x, y), x, y).Compile();
    public static Func<T, T> Lambda(Unary op) => Expression.Lambda<Func<T, T>>(op(x), x).Compile();
}

class Scan
{
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public string Str => Console.ReadLine().Trim();
    public pair<T, U> Pair<T, U>() where T : IComparable<T> where U : IComparable<U> {
        T a; U b;
        Multi(out a, out b);
        return new pair<T, U>(a, b);
    }
    public P P {
        get {
            int a, b;
            Multi(out a, out b);
            return new P(a, b);
        }
    }
    public int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public double[] DoubleArr => StrArr.Select(double.Parse).ToArray();
    public string[] StrArr => Str.Split(new[]{' '}, StringSplitOptions.RemoveEmptyEntries);
    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    T cv<T>(string s) => eq<T, int>()    ? ct<T, int>(int.Parse(s))
                       : eq<T, long>()   ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, char>()   ? ct<T, char>(s[0])
                                         : ct<T, string>(s);
    public void Multi<T>(out T a) => a = cv<T>(Str);
    public void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
    public void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]); }
}