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 <math.h>
#include <numeric>
#include <vector>
#include <map>
#include <algorithm>
#include <set>
#include <queue>
#include <tuple>
#include <functional>
#include <cstring>

#define PI 3.14159265359
#define INF 1e9
#define LINF 1e18
#define IMOD 1000000007 
#define irep(i,n) for(int  i = 0; i < n; i++)
#define irep2(i,a,n) for(int i = a; i < n; i++)
#define lrep(i,n) for(long long  i = 0; i < n; i++)
#define lrep2(i,a,n) for(long long i = a; i < n; i++)

typedef long long ll;
typedef std::vector<int> v_int;
typedef std::vector<std::vector<int> > v2_int;
typedef std::vector<ll> v_ll;
typedef std::vector<std::vector<ll> > v2_ll;
typedef std::vector<std::string> v_string;
typedef std::vector<std::vector<std::string> > v2_string;
typedef std::pair<ll, ll> pll;

using namespace std;

int main() 
{
    ll x;
    ll ans = 0;
    cin >> x;

    irep(i, INF) {
        ans += i;
        if(ans >= x) {
            cout << i << endl;
            return 0;
        }
    }

    return 0;
}