012 Inversion

AtCoder

IDabc265_g

Time5000ms

Memory256MB

Difficulty—

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 $B_i > B_j$. ## 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. ## 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: $1$ $L$ $R$ $2$ $L$ $R$ $S$ $T$ $U$ [samples]

Samples

Input #1

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

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 $(A_2,A_3,A_4,A_5)=(2,0,1,0)$.

Input #2

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

Output #2

0
0

API Response (JSON)

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