Problem Statement

You are given $a sequence A=(A_1,\ldots,A_N)$ of length N. Each element is 0, 1, or 2.
Process Q queries in order. Each query is of one of the following kinds:

• 1 L R: print the inversion number of the sequence $(A_L,\ldots,A_R)$.
• 2 L R S T U: for each i such that $L\leq i \leq R$, if A_i is 0, replace it with S; if A_i is 1, replace it with T; if A_i is 2, replace it with U.

What is the inversion number?
The inversion number of $a sequence B = (B_1, \ldots, B_M)$ is the number of pairs of integers $(i, j) (1 \leq i < j \leq M)$ such that B_i > B_j.

Input

Input is given from Standard Input in the following format:
N Q
$A_1 A_2 \ldots A_N$
$\rm Query_1$
$\rm Query_2$
$\vdots$
$\rm Query_Q$

$\rm Query_i$ denotes the i-th query, which is in one of the following formats:
1 L R

2 L R S T U

Output

Print the responses to the queries of the first kind in the given order, separated by newlines.

Constraints

• $1 \leq N \leq 10^5$
• $0 \leq A_i \leq 2$
• $1\leq Q\leq 10^5$
• In each query, $1\leq L \leq R \leq N$.
• In each query of the second kind, $0\leq S,T,U \leq 2$.
• All values in input are integers.

Sample Input 1

5 3
2 0 2 1 0
1 2 5
2 2 4 2 1 0
1 2 5

Sample Output 1

3
4

Initially, A=(2,0,2,1,0).

• In the 1-st query, print the inversion number 3 of (A_2,A_3,A_4,A_5)=(0,2,1,0).
• The 2-nd query makes A=(2,2,0,1,0).
• In the 3-rd query, print the inversion number 4 of (A_2,A_3,A_4,A_5)=(2,0,1,0).

Sample Input 2

3 3
0 1 2
1 1 1
2 1 3 0 0 0
1 1 3

Sample Output 2

0
0

见题面 Input 部分

见题面 Output 部分