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 <bits/stdc++.h>
using namespace std;

#define FOR(i,l,r) for(int i = (int) (l);i < (int) (r);i++)
#define ALL(x) x.begin(),x.end()
template<typename T> bool chmax(T& a,const T& b){ return a < b ? (a = b,true) : false; }
template<typename T> bool chmin(T& a,const T& b){ return b < a ? (a = b,true) : false; }
typedef long long ll;

int X;

int main()
{
	scanf("%d",&X);

	int sum = 0;
	for(int i = 1;;i++){
		sum += i;
		if(sum >= X){
			printf("%d\n",i);
			break;
		}
	}

	return 0;
}