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>

#define rep(i, n) for(int i = 0; i < n; i++)

typedef long long ll;
using namespace std;
int mod = 1000000007;

int main(void){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    vector<int> fib;
    fib.push_back(0);
    fib.push_back(1);
    for(int i = 2; fib[i-1] <= 1000000000; i++){
        fib.push_back(fib[i-1]+i);
    }
    int X; cin >> X;
    int ans = 0;
    while(fib[ans] < X) ans++;
    cout << ans << endl;
    return 0;
}