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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author anand.oza
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CTwoAlpinists solver = new CTwoAlpinists();
        solver.solve(1, in, out);
        out.close();
    }

    static class CTwoAlpinists {
        private NumberTheory.Modulus<NumberTheory.Mod107> mod = new NumberTheory.Mod107();

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();

            int[] maxBefore = new int[n + 1]; // maxBefore[0] == 0

            for (int i = 0; i < n; i++) {
                maxBefore[i + 1] = in.nextInt();
            }

            int[] maxAfter = new int[n + 1]; // maxAfter[n] == 0

            for (int i = 0; i < n; i++) {
                maxAfter[i] = in.nextInt();
            }

            int[] min = new int[n];
            Arrays.fill(min, 1);
            int[] max = new int[n];
            Arrays.fill(max, Integer.MAX_VALUE);

            for (int i = 0; i < n; i++) {
                if (maxBefore[i + 1] != maxBefore[i]) {
                    min[i] = Math.max(min[i], maxBefore[i + 1]);
                }
                max[i] = Math.min(max[i], maxBefore[i + 1]);

                if (maxAfter[i] != maxAfter[i + 1]) {
                    min[i] = Math.max(min[i], maxAfter[i]);
                }
                max[i] = Math.min(max[i], maxAfter[i]);
            }

            NumberTheory.ModularNumber<NumberTheory.Mod107> answer = mod.create(1);
            for (int i = 0; i < n; i++) {
                answer = answer.mult(max[i] - min[i] + 1);
            }

            out.println(answer);
        }

    }

    static class NumberTheory {
        public abstract static class Modulus<M extends NumberTheory.Modulus<M>> {
            public abstract long modulus();

            public NumberTheory.ModularNumber<M> create(long value) {
                return new NumberTheory.ModularNumber(value, this);
            }

        }

        public static class Mod107 extends NumberTheory.Modulus<NumberTheory.Mod107> {
            public long modulus() {
                return 1_000_000_007L;
            }

        }

        public static class ModularNumber<M extends NumberTheory.Modulus<M>> {
            public final long value;
            public final M m;
            public final long MOD;

            public ModularNumber(long value, M m) {
                this.m = m;
                this.MOD = m.modulus();
                this.value = (value % MOD + MOD) % MOD;
            }

            public NumberTheory.ModularNumber<M> mult(long other) {
                return m.create(value * other);
            }

            public String toString() {
                return String.valueOf(value);
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}