Range Minimum Query and Update

You are given an array of n integers and q queries. There are two types of queries:

• Update Query: 1 x y – update the element at position x (1-indexed) to the value y.
• Range Minimum Query: 2 l r – find the minimum element in the range from l to r (inclusive).

For each query of the second type, output the minimum element in the specified range. If there are no range queries, output nothing.

Note: The queries are provided in order. The array indices are 1-indexed.

The fundamental idea behind an efficient solution is to use a segment tree which supports both range queries and point updates in O(log n) time.

The mathematical definition of the range minimum query can be stated in LaTeX as follows:

$$ \min_{i=l}^{r} a_i $$

inputFormat

The input is read from stdin and consists of the following:

• The first line contains two integers n and q — the number of elements in the array and the number of queries.
• The second line contains n space-separated integers representing the initial array.
• The next q lines each contain a query in one of the two formats described above.

outputFormat

For each range minimum query (queries of type 2), output the minimum value found in the specified range on a new line. The output is written to stdout.

## sample

5 5
5 4 3 2 1
2 1 5
1 3 9
2 1 5
2 3 4
1 5 0

1
1
2

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