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 <string>
#include <vector>
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <cctype>
#define len length()
#define sz size()
#define rng(i, a, b) for(int i = a; i < b; i++)
#define rep(i, n) rng(i, 0, n)
#define srt(v) sort(v.begin(), v.end())
#define rev(s) reverse(s.begin(), s.end())
#define vi(a, n) vector<int> a(n)
#define vs(a, n) vector<string> a(n)
#define vc(a, n) vector<char> a(n)
#define psb(a) push_back(a)
#define ppb pop_back()
#define erc(S, i) S.erase(S.begin() + i)
#define ers(S, i, j) S.erase(S.begin() + i, S.begin() + j)
#define sp(n) cout << setprecision(n) << fixed
#define fst(s) s.at(0)
#define lst(s) s.at(s.len - 1)
using namespace std;

int main(){
    int X;
    cin >> X;
    int count=0;
    int i=0;
    while(count<X){
        count+=i;
        i++;
    }
    cout << i - 1 << endl;
    return 0;

}