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)

mod segtree {
    pub trait Monoid {
        type Elem;
        fn id(&self) -> Self::Elem;
        fn ops(&self, lhs: &Self::Elem, rhs: &Self::Elem) -> Self::Elem;
    }

    pub struct SegmentTree<T: Monoid> {
        v: Vec<T::Elem>,
        n: usize,
        t: T,
    }

    impl<T: Monoid> SegmentTree<T>
    where
        T::Elem: ::std::clone::Clone,
    {
        pub fn new(n: usize, t: T) -> SegmentTree<T> {
            let mut st = SegmentTree {
                n: 1,
                t: t,
                v: Vec::new(),
            };
            while st.n < n {
                st.n *= 2;
            }
            st.v.resize(st.n * 2 - 1, st.t.id());
            if n >= 2 {
                for i in 0..st.n - 2 + 1 {
                    let i = st.n - 2 - i;
                    st.v[i] = st.t.ops(&st.v[i * 2 + 1], &st.v[i * 2 + 2]);
                }
            }
            st
        }
        #[allow(dead_code)]
        pub fn set(&mut self, i: usize, x: T::Elem) {
            let mut i = i + self.n - 1;
            self.v[i] = x;
            while i > 0 {
                i = (i - 1) / 2;
                self.v[i] = self.t.ops(&self.v[i * 2 + 1], &self.v[i * 2 + 2]);
            }
        }
        #[allow(dead_code)]
        pub fn get(&self, a: usize, b: usize) -> T::Elem { self.q(a, b, 0, 0, self.n) }

        fn q(&self, a: usize, b: usize, k: usize, l: usize, r: usize) -> T::Elem {
            if r <= a || b <= l {
                self.t.id()
            } else if a <= l && r <= b {
                self.v[k].clone()
            } else {
                let c = (l + r) / 2;
                self.t.ops(
                    &self.q(a, b, k * 2 + 1, l, c),
                    &self.q(a, b, k * 2 + 2, c, r),
                )
            }
        }
    }

    impl<T: Monoid> ::std::ops::Index<usize> for SegmentTree<T> {
        type Output = T::Elem;
        #[allow(dead_code)]
        fn index(&self, i: usize) -> &Self::Output { &self.v[i] }
    }
}

struct MinMonoid {}
impl segtree::Monoid for MinMonoid {
    type Elem = u64;
    fn id(&self) -> Self::Elem { (1u64 << 31) - 1 }
    fn ops(&self, lhs: &Self::Elem, rhs: &Self::Elem) -> Self::Elem { std::cmp::min(*lhs, *rhs) }
}

#[allow(unused_imports)]
use std::io;

#[allow(dead_code)]
fn read_line() -> String {
    let mut s = String::new();
    io::stdin().read_line(&mut s).unwrap();
    s
}

#[allow(unused_macros)]
macro_rules! from_line {
    ($($a:ident : $t:ty),+) => {
        $(let $a: $t;)+
        {
            let _line = read_line();
            let mut _it = _line.trim().split_whitespace();
            $($a = _it.next().unwrap().parse().unwrap();)+
            assert!(_it.next().is_none());
        }
    };
}

fn main() {
    from_line!(n: usize, q: usize);
    let mut st = segtree::SegmentTree::new(n, MinMonoid {});
    for _ in 0..q {
        from_line!(comp: usize, x: usize, y: usize);
        match comp {
            0 => st.set(x, y as u64),
            1 => println!("{}", st.get(x, y + 1)),
            _ => unreachable!(),
        };
    }
}