Problem:
Range Minimum Query (RMQ)

Write a program which manipulates a sequence A = {a0, a1, . . . , an-1} with the following operations:

find(s, t): report the minimum element in as, as+1, . . . ,at.

update(i, x): change ai to x.

Note that the initial values of ai (i = 0, 1, . . . , n−1) are 231-1.

Input

n q
com0 x0 y0
com1 x1 y1
...
comq−1 xq−1 yq−1

In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, q queries are given where com represents the type of queries. '0' denotes update(xi, yi) and '1' denotes find(xi, yi).

Output

For each find operation, print the minimum element.

Constraints

1 ≤ n ≤ 100000

1 ≤ q ≤ 100000

If comi is 0, then 0 ≤ xi < n, 0 ≤ yi < 231-1.

If comi is 1, then 0 ≤ xi < n, 0 ≤ yi < n.

Sample Input 1

3 5
0 0 1
0 1 2
0 2 3
1 0 2
1 1 2

Sample Output 1

1
2

Sample Input 2

1 3
1 0 0
0 0 5
1 0 0

Sample Output 2

2147483647
5

Solution in Rust (judge verdict: Accepted)

trait Monoid {
    type T: Clone;
    fn id() -> Self::T;
    fn op(a: &Self::T, b: &Self::T) -> Self::T;
}

#[derive(Debug)]
struct SegmentTree<M: Monoid> {
    n: usize,
    vec: Vec<M::T>,
}

impl<M: Monoid> SegmentTree<M> {
    fn new(n: usize) -> Self {
        let n = n.next_power_of_two();
        SegmentTree {
            n: n,
            vec: vec![M::id().clone(); 2 * n - 1],
        }
    }

    // vec[k] = a
    fn update(&mut self, k: usize, a: M::T) {
        let mut k = k + self.n - 1;
        self.vec[k] = a;
        while k > 0 {
            k = (k - 1) / 2;
            self.vec[k] = M::op(&self.vec[2 * k + 1], &self.vec[2 * k + 2]);
        }
    }

    fn querySub(&self, a: usize, b: usize, k: usize, l: usize, r: usize) -> M::T {
        if r <= a || b <= l {
            M::id()
        } else if a <= l && r <= b {
            self.vec[k].clone()
        } else {
            M::op(
                &self.querySub(a, b, k * 2 + 1, l, (l + r) / 2),
                &self.querySub(a, b, k * 2 + 2, (l + r) / 2, r),
            )
        }
    }

    // op [a, b)
    fn query(&self, a: usize, b: usize) -> M::T {
        self.querySub(a, b, 0, 0, self.n)
    }
}

struct MIN;
impl Monoid for MIN {
    type T = i64;
    fn id() -> Self::T {
        2_i64.pow(31) - 1
    }
    fn op(a: &Self::T, b: &Self::T) -> Self::T {
        std::cmp::min(*a, *b)
    }
}

use std::io::*;
use std::str::FromStr;

fn main() {
    let n: usize = read();
    let q: usize = read();
    let mut seg: SegmentTree<MIN> = SegmentTree::new(n);
    for _ in 0..q {
        let com: usize = read();
        let x: usize = read();
        let y: usize = read();
        if com == 0 {
            seg.update(x, y as i64);
        } else {
            println!("{}", seg.query(x, y + 1));
        }
    }
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}