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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<iostream>
#include<unordered_map>
#include<bitset>
#include<math.h>
#include<vector>
#include<set>
#include<algorithm>
#include<ctype.h>
#include<unordered_set>
#include<string>
#include<iomanip>
#include<queue>
#include<limits>
#include<map>
#include<stack>
#include<iterator>
#include<cstring>
 
#include<deque>
#define pi 3.141592653589793238
#include<chrono>
#pragma GCC target ("avx2")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")
#define MOD 1000000007
#define INF 999999999999999999 
#define pb push_back
#define ff first
#define ss second
 
#define mt make_tuple
#define ll long long
#define fast ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>

using namespace __gnu_pbds;
 
 
typedef tree<ll, null_type, less_equal<ll>, rb_tree_tag, tree_order_statistics_node_update> indexed_set;
 
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 
int main() {
    //freopen("input.txt", "r", stdin);
    //freopen("output.txt", "w", stdout);
    fast;
    ll T = 1, i, j;
    
    //cin >> T;
    while (T--) {
        ll n;
        cin >> n;
        ll x = (-1 + sqrt(1 + 8 * n)) / 2;
        if(x * (x + 1) == 2 * n){

        }
        else{
            x++;
        }
        cout << x;
    }
    return 0;
}