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 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:

```
$1$ $L$ $R$
```
```
$2$ $L$ $R$ $S$ $T$ $U$
```

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

-   $1 \leq N \leq 10^5$
-   $0 \leq A_i \leq 2$
-   $1\leq Q\leq 10^5$
-   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.

3
4

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

• In the 1-st query, print the inversion number 3 of (A2,A3,A4,A5)=(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 (A2,A3,A4,A5)=(2,0,1,0).