Range Query - Range Minimum Query (RMQ)

Time Limit : 2 sec, Memory Limit : 131072 KB
Japanese version is here

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 mimimum 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