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 Rust (1.15.1) (judge verdict: Time Limit Exceeded)

macro_rules! input {
    ($ttype:ty) => {
        {
            let mut input = String::new();
            let _= std::io::stdin().read_line(&mut input);
            input.trim().parse::<$ttype>().unwrap()
        }
    };

    ($($ttype:ty),*) => {
        {
            use std::io::BufRead;
            let mut input = String::new();
            let stdin = std::io::stdin();
            let _ = stdin.lock().read_line(&mut input);
            let mut iter = input.trim().split_whitespace();
            (
                $(iter.next().unwrap().parse::<$ttype>().unwrap(),)*
            )
        }
    };

    ($ttype:ty; $x:expr) => {
        {
            use std::io::BufRead;
            let mut input = String::new();
            let stdin = std::io::stdin();
            let _ = stdin.lock().read_line(&mut input);
            let v: Vec<$ttype> = input
                .trim()
                .split_whitespace()
                .map(|x| x.parse().unwrap())
                .collect();
            v
        }
    };

    ($ttype:ty; $x:expr; $y:expr) => {
        {
            use std::io::BufRead;
            let mut matrix = Vec::with_capacity($y);
            for _ in 0..$y {
                let mut input = String::new();
                let stdin = std::io::stdin();
                let _ = stdin.lock().read_line(&mut input);
                let v: Vec<$ttype> = input
                    .trim()
                    .split_whitespace()
                    .map(|x| x.parse().unwrap())
                    .collect();
                matrix.push(v);
            }
            matrix
        }
    };
}


fn main() {
    let x = input!(i64);

    let t = 1;
    loop {
        if t * (t + 1) / 2 >= x {
            println!("{}", t);
            break;
        }
    }
}