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 Haskell (judge verdict: Accepted)

import Control.Monad
import Control.Applicative
import Data.Maybe
import qualified Data.ByteString.Char8 as B

data Tree = E | T Int Tree Tree
inf = 2^31-1
n_ = 2^17

root = T inf root root

val (T x _ _) = x
val E = inf

update (T _ left right) k x l r
    | r - l == 1 = T x E E
    | k < mid =
        let newleft = update left k x l mid
        in T (min (val newleft) (val right)) newleft right
    | otherwise =
        let newright = update right k x mid r
        in T (min (val left) (val newright)) left newright
    where mid = (l + r) `div` 2

query (T val left right) a b l r
    | b <= l || r <= a = inf
    | a <= l && r <= b = val
    | otherwise = min (query left a b l mid) (query right a b mid r)
    where mid = (l + r) `div` 2

solve [] _ = []
solve ([t,x,y]:qs) tree = case t of
    0 -> solve qs (update tree x y 0 n_)
    1 -> (query tree x (y + 1) 0 n_):(solve qs tree)

main = do
    _ <- getLine
    qs <- map (map (fst . fromJust . B.readInt) . B.words) . B.lines <$> B.getContents
    mapM_ print $ solve qs root