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F. Machine Learning

time limit per test

4 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputYou come home and fell some unpleasant smell. Where is it coming from?

You are given an array *a*. You have to answer the following queries:

- You are given two integers
*l*and*r*. Let*c*_{i}be the number of occurrences of*i*in*a*_{l: r}, where*a*_{l: r}is the subarray of*a*from*l*-th element to*r*-th inclusive. Find the Mex of {*c*_{0},*c*_{1}, ...,*c*_{109}} - You are given two integers
*p*to*x*. Change*a*_{p}to*x*.

The Mex of a multiset of numbers is the smallest non-negative integer not in the set.

Note that in this problem all elements of *a* are positive, which means that *c*_{0} = 0 and 0 is never the answer for the query of the second type.

Input

The first line of input contains two integers *n* and *q* (1 ≤ *n*, *q* ≤ 100 000) — the length of the array and the number of queries respectively.

The second line of input contains *n* integers — *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{9}).

Each of the next *q* lines describes a single query.

The first type of query is described by three integers *t*_{i} = 1, *l*_{i}, *r*_{i}, where 1 ≤ *l*_{i} ≤ *r*_{i} ≤ *n* — the bounds of the subarray.

The second type of query is described by three integers *t*_{i} = 2, *p*_{i}, *x*_{i}, where 1 ≤ *p*_{i} ≤ *n* is the index of the element, which must be changed and 1 ≤ *x*_{i} ≤ 10^{9} is the new value.

Output

For each query of the first type output a single integer — the Mex of {*c*_{0}, *c*_{1}, ..., *c*_{109}}.

Example

Input

10 4

1 2 3 1 1 2 2 2 9 9

1 1 1

1 2 8

2 7 1

1 2 8

Output

2

3

2

Note

The subarray of the first query consists of the single element — 1.

The subarray of the second query consists of four 2s, one 3 and two 1s.

The subarray of the fourth query consists of three 1s, three 2s and one 3.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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