Student Score Queries

You are given the scores of ( n ) students and ( q ) operations. Each operation is of one of the following types:

1. Update the score of the student at a given index to a new value.
2. Query the maximum score in the range between two given indices.

For an update operation, the input is formatted as:

1 i x

which sets the score of the ( i^{th} ) student to ( x ). The query operation is formatted as:

2 l r

which requires you to output the maximum score in the range from index ( l ) to index ( r ). Formally, the query asks for the computation of:

[ \max{ s_i : l \le i \le r } ]

Your task is to process all operations sequentially and output the result of each query operation on a separate line. The input is read from standard input and the output should be printed to standard output.

inputFormat

The first line contains two integers ( n ) and ( q ), where ( n ) is the number of students and ( q ) is the number of operations. The second line contains ( n ) integers representing the initial scores of the students. The next ( q ) lines each describe an operation. Each operation is in one of the following formats:

• For an update operation: 1 i x where ( i ) (1-indexed) is the student index and ( x ) is the new score.
• For a query operation: 2 l r where ( l ) and ( r ) (1-indexed) specify the inclusive range for the query.

outputFormat

For each query operation, output a single integer which is the maximum score in the specified range. Each result should be printed on a new line.## sample

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

3
6
6