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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bitset>
#include<math.h>
#include<limits.h>
#include<iostream>
#include<string>
#include<vector>
#include<stdio.h>
#include<sstream>
#include<list>
#include<queue>
#include<algorithm>
#include<functional>
#include<map>
#include<set>
#include<utility>
#include<initializer_list>
#include<tuple>
#include<regex>
using namespace std;
#define ull unsigned long long
#define ll long long
#define rep(i, n) for(int i=0;i<(int)(n);i++)
#define rep1n(i, n) for(int i=1;i<=(int)(n);i++)
#define all(t) t.begin(), t.end()
#define rall(t) t.rbegin(), t.rend()
#define mat(type, row, col, init) vector<vector<type>>(row, vector<type>(col, init));
#define Yes(cond) cout<<(cond? "Yes":"No")<<endl;
#define YES(cond) cout<<(cond? "YES":"NO")<<endl;
int main() {

	ll x;
	cin >> x;

	ll sum = 0;
	rep(i, x+1) {
		sum = i*(i + 1) / 2;
		if (sum >= x) {
			cout << i << endl;
			break;
		}
	}
	return 0;
}