Permutation Query

An array of integers $p_1,p_2,....,p_n$ is called a permutation if it contains each number from $1$ to $n$ exactly once. For example, the following arrays are permutations: $[3,1,2], [1], [1,2,3,4,5]$ and $[4,3,1,2]$. The following arrays are not permutations: $[2], [1,1], [2,3,4]$.

You are given an array of $n$ elements and $q$ queries. These queries are of two types:

• $1 \, \, l \, \, r$ means, if $A_l,A_{l+1},A_{l+2},,,,A_{r-1},A_r$ holds permutation, then print YES. Otherwise, print NO.

• $2 \text{ pos val}$ means, set $A_{pos}=val.$

Input

The first line contains two integer $n$ and $q$$(1\leq n,q \leq 2\times10^{5})$the size of the array and the number of queries.

The second line contains $n$ integer $A_1,A_2,....,A_n$$(1\leq A_i\leq n)$.

The next $q$ lines contain two types of queries.

$Type_i \in \{1, 2\}$

$1\leq l_i\leq r_i\leq n$

$1\leq pos_i, val_i \leq n$

Output

For every query of type $1$, print YES if $l$ to $r$ holds a permutation. Otherwise, print NO.

Sample

Input	Output
5 4 2 1 3 4 5 1 1 5 2 4 3 1 1 5 1 1 3	YES NO YES
Initially, the array looks like this [2,1,3,4,5]. After the second query, the array becomes [2,1,3,3,5].