XORin and XORmin are fighting for the title of

Help XORin and XORmin answer the Great Wise Man's questions.

*Great Wise Man's Succesor*. They want to prove their skills in graph theoryby solving the following task:*Given N nodes you have to perform M operations:*

1 a b : an undirected edge is added between nodes a and b.

2 a: Delete the a

3 a b : find out whether we can add some edges (possibly none) such that1 a b : an undirected edge is added between nodes a and b.

2 a: Delete the a

^{th}added edge (1 based indexing)3 a b : find out whether we can add some edges (possibly none) such that

**only**the nodes a, a+1, ... b-1, b form a connected component.Help XORin and XORmin answer the Great Wise Man's questions.

## Input

On the first line there will be the numbers N and M separated by spaces. The next M lines contain information about the operations.## Output

You have to print several lines. Line i will contain the answer for the i^{th}question. The answer will be "YES" or "NO" without quotes.## Constraints

**1 ≤ N ≤ 100 000****1 ≤ M ≤ 400 000**## Sample

Input | Output |
---|---|

5 4 1 1 2 1 2 3 3 1 4 3 1 2 | YES NO |