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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#define ll long long
#define rep(i,n) for(ll i=0;i<(n);i++)
#define max(p,q) ((p)>(q)?(p):(q))
#define min(p,q) ((p)<(q)?(p):(q))
#define chmax(a,b) ((a)=(a)>(b)?(a):(b))
#define chmin(a,b) ((a)=(a)<(b)?(a):(b))
#define abs(p) ((p)>=(0)?(p):(-(p)))
#define MOD 1000000007
ll powll(ll a,ll b){ll r=1;rep(i,b){r*=a;}return r;}
#define swap(a,b) do{ll w=(a);(a)=(b);(b)=w;}while(0)
#define swapd(a,b) do{double w=(a);(a)=(b);(b)=w}while(0)
#define in(a) scanf("%lld", &(a))
#define in2(a,b) scanf("%lld %lld",&(a),&(b))
#define in3(a,b,c) scanf("%lld %lld %lld",&(a),&(b),&(c))
#define ind(a) scanf("%lf", &(a))
#define ins(a) scanf("%s", (a))
#define inc(a) scanf("%c", &(a))
#define put(a) printf("%lld\n", (a))
#define putd(a) printf("%.15f\n", (a))
//      puts(a) printf("%s\n", a) 文字はこっち
//your code here!
int main(void){
    ll X;
    in(X);
    for(ll i=1; ; i++){
        if(i*(i+1)/2>=X){
            put(i);
            return 0;
        }
    }
}