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: Time Limit Exceeded)

import Data.IntMap ((!))
import qualified Data.IntMap.Strict as M
import qualified Data.ByteString.Char8 as B
import Data.List
import Data.Maybe
import Control.Applicative

main = do
 [n,_] <- map read . words <$> getLine
 cxys <- map ((\[c,x,y]->(c,(x,y))) . map (fst . fromJust . B.readInt) . B.words) . B.lines <$> B.getContents
 mapM_ print (rmq n cxys)

rmq :: Int -> [(Int,(Int,Int))] -> [Int]
rmq n = reverse . fst . foldl' process ([], M.empty)

process (lg,m) (c,(x,y))
 | c==0 = (lg, M.insert x y m)
 | c==1 = (minimum (map (\i -> M.findWithDefault (2^31-1) i m) [x..y]) : lg, m)