There is a melon stall with $m$ melons, numbered from $1$ to $m$. There are $n$ events occurring in sequence, each being one of the following two types:

• 1 l r where $1\leqslant l \leqslant r \leqslant m$: A student arrives wanting to purchase all melons with indices in the range $[l, r]$. To satisfy this student, all melons in $[l, r]$ must be provided.
• 2 l r where $1\leqslant l \leqslant r \leqslant m$: The students make an inquiry to the stall owner. Following the principle that "one melon can be sold to at most one student," and considering only melons with indices in $[l, r]$, inquire about the maximum number of student requests that can be satisfied. Since the students are just being difficult, they are only inquiring and will not actually purchase the melons; the inquiries are independent of each other.

If the stall owner answers incorrectly or cannot answer, the students will think the owner is hiding something, and the consequences will be severe!

As a friend of the stall owner, Liu Huaqiang, please help him.

Brief Problem Statement: There are $n$ operations, each being one of the following:

• 1 l r: Add the interval $[l, r]$, where $1\leqslant l \leqslant r \leqslant m$.
• 2 l r: Query the interval $[l, r]$, where $1\leqslant l \leqslant r \leqslant m$, to find the maximum number of disjoint intervals that are contained within $[l, r]$.

We say an interval $[l_1, r_1]$ is contained within $[l_2, r_2]$ if and only if $l_2\leqslant l_1 \leqslant r_1 \leqslant r_2$.

Input

The first line contains two integers $n$ and $m$.

The next $n$ lines each contain three integers $opt, l, r$.

Output

For each type 2 operation, output a single integer on a new line.

Examples

Input 1

16 16
2 3 4
1 3 7
2 1 3
2 1 16
1 1 5
1 9 10
2 5 16
1 2 6
2 5 13
1 11 12
2 7 11
2 4 9
1 13 14
1 15 16
1 4 8
2 4 13

Output 1

0
0
1
1
1
1
0
3

Input 2

16 16
1 2 4
2 3 10
1 13 15
1 7 9
1 3 5
2 1 16
2 3 8
2 1 13
1 8 10
2 8 8
2 6 9
2 6 16
1 5 7
2 3 3
1 8 10
2 8 8

Output 2

0
3
1
2
0
1
2
0
0

Constraints

For $20\%$ of the data, $n, m \leqslant 2 \times 10^3$.

For $50\%$ of the data, $n, m \leqslant 8 \times 10^4$.

For $100\%$ of the data, $n, m \leqslant 3 \times 10^5$, $1\leqslant opt \leqslant 2$.