MNYC '17: Bells

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Points: 17 (partial)
Time limit: 1.0s
Memory limit: 256M

Problem type

There are N (1 \le N \le 100\,000) bells arranged in a line, labelled 1 to N. The i^\text{th} bell has a frequency of f_i Hz (1 \le f_i \le 10^8). There are Q (1 \le Q \le 50\,000) operations to perform.

There are two types of operations:

  • 1 i f Replace the i^\text{th} bell with one with a frequency of f Hz.
  • 2 l r Output the number of distinct frequencies between the l^\text{th} and r^\text{th} bell (inclusive).

There will be at most 1000 distinct frequencies at a time.

Fast input may be required.


For 10% of the points, 1 \le N, Q \le 100.

For 90% of the points, 1 \le N \le 100\,000, 1 \le Q \le 50\,000.

Input Specification

The first line contains two space separated integers, N Q, respectively the number of bells and the number of queries.

The next line contains N space separated integers, the frequency of the bells.

The next Q lines each contain a query in the format described above.

Output Specification

Output a single integer on its own line for each type 2 query.

Sample Input

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

Sample Output


Explanation for Sample Output

In the beginning, there are only 3 distinct frequencies which the bells have, 1 Hz, 2 Hz, and 4 Hz. After switching the second bell with one with a frequency of 1 Hz. There is only one distinct frequency among the first 3 bells.


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