Given an array of $n$ integers, your task is to process $q$ queries of the following types:

1. update the value at position $k$ to $u$
2. what is the minimum value in range $[a,b]$?

Input

The first input line has two integers $n$ and $q$: the number of values and queries.

The second line has $n$ integers $x_1,x_2,\dots,x_n$: the array values.

Finally, there are $q$ lines describing the queries. Each line has three integers: either "$1$ $k$ $u$" or "$2$ $a$ $b$".

Output

Print the result of each query of type 2.

Constraints

• $1 \le n,q \le 2 \cdot 10^5$
• $1 \le x_i, u \le 10^9$
• $1 \le k \le n$
• $1 \le a \le b \le n$

Example

Input:

8 4
3 2 4 5 1 1 5 3
2 1 4
2 5 6
1 2 3
2 1 4

Output:

2
1
3