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.

Examples

Input

5
1 3 3 3 3
3 3 2 2 2


Output

4


Input

5
1 1 1 2 2
3 2 1 1 1


Output

0


Input

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


Output

884111967


Input

1
17
17


Output

1
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		final Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long mod = 1000000007;
		long taka[] = new long[n+2];
		long ao[] = new long[n+2];
		for(int i = 1; i <= n; i++) {
			taka[i] = sc.nextLong();
		}
		taka[0]=0;taka[n+1]=taka[n];
		for(int i = 1; i <= n; i++) {
			ao[i] = sc.nextLong();
		}
		ao[0]=ao[1];ao[n+1]=0;
		long ans = 1L;
		for(int i = 1; i <= n; i++) {
			if(taka[i-1]<taka[i]&&ao[i]>ao[i+1]) {//両方更新されている場合
				if(taka[i]==ao[i]) {
					//nothing
				} else {
					System.out.println(0);
					return;
				}
			} else if(taka[i-1]<taka[i]&&ao[i]==ao[i+1]) {
				//nothing ans *= 1;
				if(taka[i] <= ao[i]) {
					//nothing
				} else {
					System.out.println(0);
					return;
				}
			} else if(taka[i-1]==taka[i]&&ao[i]>ao[i+1]) {
				//nothing
				if(ao[i] <= taka[i]) {
					//nothing
				} else {
					System.out.println(0);
					return;
				}
			} else if(taka[i-1]==taka[i]&&ao[i]==ao[i+1]) {
				ans *= Math.min(taka[i], ao[i]);
				ans %= mod;
			} else {
				System.out.println(0);
				return;
			}
		}
		System.out.println(ans%mod);
	}
}
