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)

use std::io::stdin;

#[allow(unused_variables)]
fn main() {
    let x = input_ints()[0];

    let mut n = x / 2;
    let mut m = n / 2;

    loop {
        let cur = n * (n + 1) / 2;
        if cur - n < x && x <= cur {
            println!("{}", n);
            break;
        }

        if cur < x {
            n += m;
            m /= 2;
        } else {
            n -= m;
            m /= 2
        }
    }
}

#[allow(dead_code)]
fn input_ints() -> Vec<i64> {
    let mut st = String::new();
    match stdin().read_line(&mut st) {
        Ok(_) => st.split_whitespace().map(|s| s.parse().unwrap()).collect(),
        Err(_) => Vec::<i64>::new(),
    }
}

#[allow(dead_code)]
fn input_strs() -> Vec<String> {
    let mut st = String::new();
    match stdin().read_line(&mut st) {
        Ok(_) => st.split_whitespace().map(|s| s.to_string()).collect(),
        Err(_) => Vec::<String>::new(),
    }
}