Problem Statement

You are given two int[]s L and R, each of length n.

Find the number of strictly increasing sequences of integers A[0] < A[1] < ... < A[n-1] such that L[i] ≤ A[i] ≤ R[i] for every i. Return this number modulo 998244353.

Definition

Class:	IncreasingSequencesEasy
Method:	count
Parameters:	int[], int[]
Returns:	int
Method signature:	int count(int[] L, int[] R)
(be sure your method is public)

Limits

Time limit (s):	2.000
Memory limit (MB):	256

Notes

-

The number 998244353 is a prime number.

Constraints

-

n will be between 1 and 300, inclusive.

-

L will contain exactly n elements.

-

R will contain exactly n elements.

-

L[i] will be between 1 and 10⁴, inclusive.

-

R[i] will be between L[i] and 10⁴, inclusive.

Examples

0)

{1, 3, 1, 4}

{6, 5, 4, 6}

Returns: 4

There are 4 strictly increasing sequences satisfying the conditions: {1, 3, 4, 5}, {1, 3, 4, 6}, {2, 3, 4, 5} and {2, 3, 4, 6}.

1)

{10, 20}

{20, 30}

Returns: 120

2)

{20, 10}

{30, 20}

Returns: 0

3)

{4, 46, 46, 35, 20, 77, 20}

{41, 65, 84, 90, 49, 86, 88}

Returns: 2470