Problem:
Score : 400 points

Problem Statement

Mountaineers Mr. Takahashi and Mr. Aoki recently trekked across a certain famous mountain range.
The mountain range consists of N mountains, extending from west to east in a straight line as Mt. 1, Mt. 2, ..., Mt. N.
Mr. Takahashi traversed the range from the west and Mr. Aoki from the east.

The height of Mt. i is h_i, but they have forgotten the value of each h_i.
Instead, for each i (1 ≤ i ≤ N), they recorded the maximum height of the mountains climbed up to the time they reached the peak of Mt. i (including Mt. i).
Mr. Takahashi's record is T_i and Mr. Aoki's record is A_i.

We know that the height of each mountain h_i is a positive integer.
Compute the number of the possible sequences of the mountains' heights, modulo 10^9 + 7.

Note that the records may be incorrect and thus there may be no possible sequence of the mountains' heights.
In such a case, output 0.

Constraints

1 ≤ N ≤ 10^5

1 ≤ T_i ≤ 10^9

1 ≤ A_i ≤ 10^9

T_i ≤ T_{i+1} (1 ≤ i ≤ N - 1)

A_i ≥ A_{i+1} (1 ≤ i ≤ N - 1)

Input

The input is given from Standard Input in the following format:

N
T_1 T_2 ... T_N
A_1 A_2 ... A_N

Output

Print the number of possible sequences of the mountains' heights, modulo 10^9 + 7.

Sample Input 1

5
1 3 3 3 3
3 3 2 2 2

Sample Output 1

4

The possible sequences of the mountains' heights are:

1, 3, 2, 2, 2

1, 3, 2, 1, 2

1, 3, 1, 2, 2

1, 3, 1, 1, 2

for a total of four sequences.

Sample Input 2

5
1 1 1 2 2
3 2 1 1 1

Sample Output 2

0

The records are contradictory, since Mr. Takahashi recorded 2 as the highest peak after climbing all the mountains but Mr. Aoki recorded 3.

Sample Input 3

10
1 3776 3776 8848 8848 8848 8848 8848 8848 8848
8848 8848 8848 8848 8848 8848 8848 8848 3776 5

Sample Output 3

884111967

Don't forget to compute the number modulo 10^9 + 7.

Sample Input 4

1
17
17

Sample Output 4

1

Some mountain ranges consist of only one mountain.

Solution in Go (1.6) (judge verdict: Wrong Answer)

///
// File:  c.go
// Author: ymiyamoto
//
// Created on Sat May 26 17:04:42 2018
//
package main

import (
	"fmt"
)

const MOD int64 = 1e9 + 7

var N int
var T, A []int64

func max(a, b int64) int64 {
	if a < b {
		return b
	}
	return a
}

func min(a, b int64) int64 {
	if a < b {
		return a
	}
	return b
}

func main() {
	fmt.Scan(&N)
	T = make([]int64, N)
	A = make([]int64, N)

	max_t := int64(0)
	for i := range T {
		fmt.Scan(&T[i])
		max_t = max(max_t, T[i])
	}

	max_a := int64(0)
	for i := range A {
		fmt.Scan(&A[i])
		max_a = max(max_a, A[i])
	}

	if max_a != max_t {
		fmt.Println(0)
		return
	}

	dp := make([]int64, N)
	for i := range T {
		if i != 0 {
			if T[i] != T[i-1] {
				dp[i] = 1
			} else {
				dp[i] = T[i]
			}
		} else {
			dp[i] = 1
		}
	}

	dp2 := make([]int64, N)
	for i := len(A) - 1; i >= 0; i-- {
		if i != len(A)-1 {
			if A[i] != A[i+1] {
				dp2[i] = 1
			} else {
				dp2[i] = A[i]
			}
		} else {
			dp2[i] = 1
		}
	}

	ans := int64(1)
	for i := range dp {
		ans *= min(dp[i], dp2[i]) % MOD
		ans %= MOD
	}
	fmt.Println(ans)
}