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)

// clang-format off
#include <cassert>
#include <iostream>
#include <vector>
#include <algorithm>
#include <utility>
#include <set>
#include <iomanip>
#include <queue>
#include <map>
 
#define FOR(i, a, b) for(int i = (a); i < (b); i++)
#define RFOR(i, a, b) for(int i = (b)-1; i >= (a); i--)
#define rep(i, n) for(int i = 0; i < (n); i++)
#define rep1(i,n) for(int i = 1; i <= (n); i++)
#define rrep(i, n) for(int i = (n)-1; i >= 0; i--)
 
#define pb push_back
#define mp make_pair
#define fst first
#define snd second
#define show(x) cout << #x << " = " << x << endl
#define chmin(x,y) x=min(x,y)
#define chmax(x,y) x=max(x,y)
#define pii pair<int, int>
#define vi vector<int>
 
using namespace std;
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T>& p){return o<<"("<<p.first<<","<<p.second<<")";}
template<class T> ostream& operator<<(ostream& o,const vector<T>& vc){o<<"sz = "<<vc.size()<<endl<<"[";for(const T& v:vc) o<<v<<",";o<<"]";return o;}
typedef long long ll;
constexpr ll MOD = 1000000007;
 
 
 
int main()
{
    ll X;
    cin >>X;
    ll a =0;
    for(a = 1; ; a++){
        if(a *(a+1) >= 2*X){
            break;
        }
    }
    cout << a << endl;
    return 0;
}