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 F first
#define S second
#define modulo ll (1e9 + 7)

typedef long long ll;
typedef pair<int,int> pii;

void init(){
    cin.tie(0);
    cin.sync_with_stdio(0);
}

const int N = 2005, M = 26, OO = 0x3f3f3f3f;
const ll llOO = 0x3f3f3f3f3f3f3f3f;


int main(){
    init();

    ll x;  cin >> x;

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