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 OCaml (judge verdict: Accepted)

let split str delim =
  let open String in
  let rec doit s acc =
    match
      try Some (rindex s delim) with _ -> None
    with
    | None -> s :: acc
    | Some i -> doit (sub s 0 i) (sub s (i + 1) (length s - i - 1) :: acc) in
  doit str []

let parent i = int_of_float ((float_of_int (i - 1)) /. 2.)

let left i = 2*i + 1

let right i = 2*i + 2

let to_pow_of_2 n =
  let rec doit i =
    if i >= n then i
    else doit (i * 2) in
  doit 1

let update (s : int array) n i x =
  let j = n + i - 1 in
  s.(j) <- x;
  let rec doit j =
    if j > 0 then begin
      let j = parent j in
      s.(j) <- if s.(left j) < s.(right j) then s.(left j) else s.(right j);
      doit j
    end in
  doit j

let find s n a b =
  let rec doit a b k l r =
    if r <= a || b <= l then 2147483647
    else if a <= l && r <= b then s.(k)
    else min (doit a b (left k) l ((l + r) / 2)) (doit a b (right k) ((l + r) / 2) r) in
  doit a b 0 0 n

let solve n q =
  let n = to_pow_of_2 n in
  let s = Array.make (2*n-1) 2147483647 in
  let rec doit i =
    if i < q then begin
      begin match List.map int_of_string (split (read_line ()) ' ') with
      | 0 :: x :: y :: _ -> update s n x y
      | 1 :: x :: y :: _ -> Printf.printf "%d\n" (find s n x (y + 1))
      | _ -> ()
      end;
      doit (i + 1)
    end in
  doit 0

let () =
  match List.map int_of_string (split (read_line ()) ' ') with
  | [n; q] -> solve n q
  | _ -> ()