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E - Max Min

Score : $500$ points

Problem Statement

We have a number sequence $A = (A_1, A_2, \dots, A_N)$ of length $N$ and integers $X$ and $Y$. Find the number of pairs of integers $(L, R)$ satisfying all the conditions below.

• $1 \leq L \leq R \leq N$
• The maximum value of $A_L, A_{L+1}, \dots, A_R$ is $X$, and the minimum is $Y$.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq A_i \leq 2 \times 10^5$
• $1 \leq Y \leq X \leq 2 \times 10^5$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $X$ $Y$

$A_1$ $A_2$ $\dots$ $A_N$

Output

Print the answer.

4 3 1
1 2 3 1

4

$4$ pairs satisfy the conditions: $(L,R)=(1,3),(1,4),(2,4),(3,4)$.

5 2 1
1 3 2 4 1

0

No pair $(L,R)$ satisfies the condition.

5 1 1
1 1 1 1 1

15

It may hold that $X=Y$.

10 8 1
2 7 1 8 2 8 1 8 2 8

36