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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

typedef long long LL;

const int maxn = 100000;
const int mod = 1000000007;

LL a[maxn + 10], b[maxn + 10];
LL maxa, maxb, sa, sb;
int n;

LL solve() {
    if(sa != sb) return 0;
    if(maxa != maxb) return 0;
    LL ans = 1;
    LL t = maxa;
    for(int i = sa - 1; i >= 0; i--) {
        if(a[i] != t) t = a[i];
        else ans = (ans * a[i]) % mod;
    }
    t = maxb;
    for(int i = sb + 1; i < n; i++) {
        if(b[i] != t) t = b[i];
        else ans = (ans * b[i]) % mod;
    }
    return ans;
}

int main() {
    scanf("%d", &n);
    maxa = maxb = 0;
    for(int i = 0; i < n; i++) {
        scanf("%lld", &a[i]);
        if(a[i] > maxa) maxa = a[i], sa = i;
    }
    for(int i = 0; i < n; i++) scanf("%lld", &b[i]);
    for(int i = n - 1; i >= 0; i--) {
        if(b[i] > maxb) maxb = b[i], sb = i;
    }
    printf("%lld %lld\n", sa, sb);
    printf("%lld\n", solve());
    return 0;
}