Range Minimum Query (RMQ)

Write a program which manipulates a sequence A = {a₀, a₁, . . . , a_n-1} with the following operations:

• find(s, t): report the minimum element in a_s, a_s+1, . . . ,a_t.
• update(i, x): change a_i to x.

Note that the initial values of a_i (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(x_i, y_i) and '1' denotes find(x_i, y_i).

Output

For each find operation, print the minimum element.

Constraints

• 1 ≤ n ≤ 100000
• 1 ≤ q ≤ 100000
• If com_i is 0, then 0 ≤ x_i < n, 0 ≤ y_i < 2³¹-1.
• If com_i is 1, then 0 ≤ x_i < n, 0 ≤ y_i < 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

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