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 ll long long
#define inf 1000000007 //10^9+7
#define sort(vec) sort((vec).begin(),(vec).end());
#define rever(vec) reverse((vec).begin(),(vec).end());
#define unsort(vec) sort((vec)); rever((vec));
using namespace std;

ll kai(ll n) {
  ll ans=0;
  for(ll i=1;i<=n;i++) {
    ans+=i;
  }
  return ans;
}

int main() {
  ll x;
  cin>>x;
  ll ans=0;
  for(ll i=1;i<inf;i++) {
    if(x<=kai(i)) {
      cout<<i<<endl;
      break;
    }
  }
}