Echo Inventory

Time limit: 3000 msMemory limit: 256 MB

A research station keeps an array $A$ of sample identifiers. The inventory of an interval $[l,r]$ is the multiset containing $A_l, A_{l+1}, \ldots, A_r$ . The order of these values is ignored, but repeated values are kept with their multiplicities.

Two inventories of the same size are one-edit equivalent if at least one of the following conditions holds:

Their multisets are equal.
One occurrence with value $x$ can be selected from the first inventory and one occurrence with value $y$ can be selected from the second inventory so that, after discarding those two occurrences, the remaining multisets are equal.

Equivalently, changing at most one sample identifier in either inventory can make the two inventories equal. The change is only hypothetical and does not modify $A$ .

You must process point updates to $A$ and answer whether two specified interval inventories are one-edit equivalent.

Input

The first line contains two integers $N$ and $Q$ ( $1 \le N, Q \le 2 \cdot 10^5$ ), the length of the array and the number of operations.

Output

For every operation of type $2$ , print YES if the two interval inventories are one-edit equivalent. Otherwise, print NO.

Samples

Sample 1

Input

6 7
1 2 2 4 2 3
2 1 3 4 6
2 1 2 5 6
1 6 1
2 1 2 5 6
2 2 4 3 5
1 3 8
2 1 3 4 6

Output

NO
YES
YES
YES
YES

The inventories in the first comparison have more than one unmatched occurrence, so the answer is NO. The second comparison has one unmatched occurrence on each side. After setting $A_6$ to $1$ , the third comparison contains equal inventories. The fourth comparison also contains equal inventories in different orders. After setting $A_3$ to , the final comparison has only the occurrences and unmatched.

Echo Inventory

Input

Output

Samples

Sample 1

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