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 <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <string>
#include <iomanip>
#include <map>
#include <set>
#include <cmath>
#include <cstdio>
using namespace std;
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define FOR(i,m,n) for(int (i)=(m);(i)<(n);(i)++)
#define All(v) (v).begin(),(v).end()
typedef long long ll;

int main(){
    int X;
    cin >> X;
    int k=1;
    while(X>k*(k+1)/2){
        k++;
    }
    cout << k << endl;
    return 0;
}