Problem:
Score : 200 points

Problem Statement

There is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0.
During the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right.
That is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i.
The kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible.
Find the earliest possible time to reach coordinate X.

Constraints

X is an integer.

1≤X≤10^9

Input

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

X

Output

Print the earliest possible time for the kangaroo to reach coordinate X.

Sample Input 1

6

Sample Output 1

3

The kangaroo can reach his nest at time 3 by jumping to the right three times, which is the earliest possible time.

Sample Input 2

2

Sample Output 2

2

He can reach his nest at time 2 by staying at his position during the first second, and jumping to the right at the next second.

Sample Input 3

11

Sample Output 3

5

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

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;
namespace AtCoder {
    class MainClass {
        //C#7.0
        int X;
        void Solve() {
            io.i(out X);

            Mathf mat = new Mathf();

            int ans;
            for (ans = 1; ;ans++)
                if (mat.TousaSum(1, 1, ans) >= X)
                    break;

            io.o(ans);

        }

        public static void Main(string[] args) { new MainClass().Stream(); }
        IO io = new IO();
        void Stream() { Solve(); io.writeFlush(); }
    }
    class IO {
        string[] nextBuffer; int BufferCnt; char[] cs = new char[] { ' ' };
        StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()){
            AutoFlush = false };
        public IO() { nextBuffer = new string[0]; BufferCnt = 0; Console.SetOut(sw); }
        public string next() {
            if (BufferCnt < nextBuffer.Length) return nextBuffer[BufferCnt++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            BufferCnt = 0;
            return nextBuffer[BufferCnt++];
        }
        public char nextChar() { return char.Parse(next()); }
        public int nextInt() { return int.Parse(next()); }
        public long nextLong() { return long.Parse(next()); }
        public double nextDouble() { return double.Parse(next()); }
        public string[] arr() { return Console.ReadLine().Split(' '); }
        public char[] arrayChar() { return Array.ConvertAll(arr(), char.Parse); }
        public int[] arrayInt() { return Array.ConvertAll(arr(), int.Parse); }
        public long[] arrayLong() { return Array.ConvertAll(arr(), long.Parse); }
        public double[] arrayDouble() { return Array.ConvertAll(arr(), double.Parse); }
        private bool typeEQ<T, U>() { return typeof(T).Equals(typeof(U)); }
        private T convertType<T, U>(U v) { return (T)Convert.ChangeType(v, typeof(T)); }
        private T suitType<T>(string s) {
            if (typeEQ<T, int>()) return convertType<T, int>(int.Parse(s));
            if (typeEQ<T, long>()) return convertType<T, long>(long.Parse(s));
            if (typeEQ<T, double>()) return convertType<T, double>(double.Parse(s));
            if (typeEQ<T, char>()) return convertType<T, char>(char.Parse(s));
            return convertType<T, string>(s);
        }
        public void i<T>(out T v) { v = suitType<T>(next()); }
        public void i<T, U>(out T v1, out U v2) {
            var a = arr(); v1 = suitType<T>(a[0]); v2 = suitType<U>(a[1]);
        }
        public void i<T, U, V>(out T v1, out U v2, out V v3) {
            var a = arr(); v1 = suitType<T>(a[0]); v2 = suitType<U>(a[1]);
            v3 = suitType<V>(a[2]);
        }
        public void i<T, U, V, W>(out T v1, out U v2, out V v3, out W v4) {
            var a = arr(); v1 = suitType<T>(a[0]); v2 = suitType<U>(a[1]);
            v3 = suitType<V>(a[2]); v4 = suitType<W>(a[3]);
        }
        public void ini(out int[] a, int size) {
            a = new int[size]; for (int i = 0; i < size; i++) a[i] = nextInt();
        }
        public void ini(out int[] a1, out int[] a2, int size) {
            a1 = new int[size]; a2 = new int[size];
            for (int i = 0; i < size; i++) { a1[i] = nextInt(); a2[i] = nextInt(); }
        }
        public void ini(out string[] a, int size) {
            a = new string[size]; for (int i = 0; i < size; i++) a[i] = next();
        }
        public void inii(out int[] a, int size) {
            a = new int[size]; for (int i = 0; i < size; i++) a[i] = nextInt() - 1;
        }
        public void inii(out int[] a1, out int[] a2, int size) {
            a1 = new int[size]; a2 = new int[size];
            for (int i = 0; i < size; i++) { a1[i] = nextInt() - 1; a2[i] = nextInt() - 1; }
        }
        public void o<T>(T v) { Console.WriteLine(v); }
        public void o<T>(params T[] a) { foreach (T v in a) Console.WriteLine(v); }
        public void o<T>(List<T> l) { foreach (T v in l) sw.WriteLine(v); }
        public void ol<T>(T v) { Console.Write(v + " "); }
        public void ol<T>(params T[] a) { foreach (T v in a) Console.Write(v + " "); 
            Console.WriteLine(""); }
        public void YN(bool f) { Console.WriteLine(f ? "YES" : "NO"); }
        public void Yn(bool f) { Console.WriteLine(f ? "Yes" : "No"); }
        public void yn(bool f) { Console.WriteLine(f ? "yes" : "no"); }
        public void br(){Console.WriteLine("");}
        public void writeFlush() { Console.Out.Flush(); }
        public string pad0<T>(T v, int n) { return v.ToString().PadLeft(n, '0'); }
    }
    
    class Mathf {
        public int mod = 1000000007;//10^9+7
        public long Pow(long a, long b) {
            if (b == 0) return 1;
            if (b % 2 == 1) return (a % mod * Pow(a % mod, b - 1) % mod) % mod;
            else return Pow(a * a % mod, b / 2) % mod;
        }
        public long Fact(long n) { return (n != 0) ? 
            (n % mod * (Fact(n - 1) % mod) % mod) : 1; }
        public long C(long n, long r) {
            if (r == 0 || n == r) return 1;
            else return (Fact(n) % mod * Pow
                         ((Fact(n - r) % mod * Fact(r) % mod) % mod, mod - 2) % mod) % mod;
        }
        public long Sum(params long[] a) {
            return a.Aggregate((v, next) => (v % mod + next) % mod); }
        public int GCD(int a, int b) { 
            if (a < b) Swap(ref a, ref b); return b == 0 ? a : GCD(b, a % b); }
        public int GCD(int[] array) { return array.Aggregate((v, next) => GCD(v, next)); }
        public void Swap<T>(ref T a, ref T b) { T tmp = a; a = b; b = tmp; }
        public T Max<T>(params T[] v) { return v.Max(); }
        public T Min<T>(params T[] v) { return v.Min(); }
        public double Dis(int x1, int y1, int x2, int y2) {
            return Math.Sqrt(Math.Pow((x2 - x1), 2) + Math.Pow((y2 - y1), 2));
        }
        public int Digit(long n) { return (n == 0) ? 1 : (int)Math.Log10(n) + 1; }
        public int Clamp(int n, int a, int b) {return (n < a) ? a : (b < n) ? b : n;}
        public long Clamp(long n, long a, long b) {return (n < a) ? a : (b < n) ? b : n;}
        public double Clamp(double n, double a, double b) { 
            return (n < a) ? a : (b < n) ? b : n;}
        public long Tousa(long a, long d, int no) { return a + (no - 1) * d; }
        public long TousaSum(long a, long d, int no) { return no* (2 * a + (no - 1) * d) / 2; }
    }
    class AssociativeArray<T>{
        public Dictionary<T, int> dic;
        public void init(T[] a){dic = new Dictionary<T, int> ();
            for (int i = 0;i<a.Length;i++){
                if (!dic.ContainsKey(a[i])) dic[a[i]] = 0;dic[a[i]]++;}
        }
        public int ValueSum() { int s = 0; foreach (var i in dic) s += i.Value; return s; }
        public int KeyNum() { return dic.Keys.Count; }
        public int Max(){return dic.Values.Max();}
        public int Min() { return dic.Values.Min(); }
        public T MaxKey() { return dic.First(d => d.Value == Max()).Key; }
        public T MinKey() { return dic.First(d => d.Value == Min()).Key; }
        public bool isContains(T k) { return dic.ContainsKey(k); }
        //:sort->array
    }
    class Time{
        public bool isLeapYear(int y) { 
            return (y % 400 == 0 || (y % 4 == 0 && y % 100 != 0)); }
    }
    class BucketSort {
        public int[] bucket;
        public void Init(int[] a) {
            bucket = new int[a.Max() + 1];
            for (int i = 0; i < a.Length; ++i) ++bucket[a[i]];
            for (int i = 0, j = 0; j < bucket.Length; ++j)
                for (int k = bucket[j]; k != 0; --k, ++i) a[i] = j;
        }
    }

    static class StringEX {
        public static string Reversed(this string s) { return string.Join("", s.Reverse()); }
        public static string Repeat(this string s, int n) { 
            return string.Concat(Enumerable.Repeat(s, n).ToArray()); }
    }
    static class CharEX{
        public static int toInt(this char c) { return int.Parse(c.ToString()); }
    }
}