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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;
import java.math.*;
 
public class Main {
	public static void main(String[] args)throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringBuilder sb = new StringBuilder();
		int n = Integer.parseInt(br.readLine());

		String[] str1 = br.readLine().split(" ");
		String[] str2 = br.readLine().split(" ");
		int[] t = new int [n]; 
		int[] a = new int [n]; 
		int max = 0;
		int maxnum = 0;
		for(int i = 0; i < n; i++){
			t[i] = Integer.parseInt(str1[i]);
			a[i] = Integer.parseInt(str2[i]);
			if(t[i]>max && t[i]==a[i]){
				max = t[i];
				maxnum = i;
			}
		}
		// 0 check
		for(int i = maxnum; i < n; i++){
			if(max<t[i]){
				sb.append('0');
				System.out.println(sb);
				return;
			}
		}
		for(int i = maxnum; i > -1; i--){
			if(max<a[i]){
				sb.append('0');
				System.out.println(sb);
				return;
			}
		}
		// count
		int[] p = new int [n];
		p[0] = 1;
		p[n-1] = 1;
		for(int i = 1; i < n; i++){
			if(t[i]>t[i-1]){
				p[i] = 1;
			}else{
				p[i] = t[i];
			}
		}
		for(int i = n-2; i > -1; i--){
			if(a[i]>a[i+1]){
				p[i] = 1;
			}else{
				if(p[i]>a[i])
					p[i] = a[i];
			}
		}
		p[0] = 1;
		p[n-1] = 1;
		long cnt = 1;
		final long mod = 1000000007;
		for(int i = 0; i < n; i++){
			cnt = (cnt*p[i])%mod;
		}
		sb.append(cnt);
		System.out.println(cnt);
	}
}