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;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
typedef long long int ll;

#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))
#define MOD (1000000007)
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1}; // 移動方向

// dp[i] := 座標iまでにかかる時刻の最小値
ll x;

void input(){
    cin >> x;
}

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    input();
    ll i = 1;
    ll sm = 0;
    while(x > sm){
        sm += i;
        i++;
    }
    cout << i-1 << endl;
    return 0;
}