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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.InteropServices;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using static Math2;
using static Output;
using static Utils;

public class CP
{
    Input sc;
    public void Solve()
    {
        sc = new Input();
        var t = 1;
        while (t-- > 0)
        {
            Case1();
        }
    }
    public void Case1()
    {

        int n = sc.cin<int>();
        var t = sc.cinarr<int>();
        var a = sc.cinarr<int>();
        bool[] isconfirmed = new bool[n];
        isconfirmed[0] = true;
        isconfirmed[n - 1] = true;
        for (int i = 0; i < n - 1; ++i)
        {
            if (t[i] != t[i + 1]) isconfirmed[i + 1] = true;
        }
        for (int i = n - 1; i >= 1; --i)
        {
            if (a[i] != a[i - 1]) isconfirmed[i - 1] = true;
        }
        long ans = 1;
        for (int i = 0; i < n; ++i)
        {
            if (!isconfirmed[i]) ans *= Min(a[i], t[i]) % MOD;
            ans %= MOD;
        }
        for (int i = 0; i < n; ++i)
        {

        }
        Put(ans % MOD);
    }


}

public static class NumberTheory
{
    public static Dictionary<long, int> PrimeFactorization(long N)
    {
        var ret = new Dictionary<long, int>();
        for (long i = 2; i * i <= N; ++i)
        {
            int cnt = 0;
            while (N % i == 0)
            {
                cnt++;
                N /= i;
            }
            if (cnt != 0) ret[i] = cnt;
        }
        if (N >= 2) ret[N] = 1;
        return ret;
    }
    public static Dictionary<int, int> FactoricalPF(int N)
    {
        var ret = new Dictionary<int, int>();
        for (int i = 2; i <= N; ++i)
        {
            int ni = i;
            for (int j = 2; j * j <= ni; ++j)
            {
                int cnt = 0;
                while (ni % j == 0)
                {
                    ++cnt;
                    ni /= j;
                }
                if (cnt == 0) continue;
                if (ret.ContainsKey(j))
                    ret[j] += cnt;
                else ret[j] = cnt;
            }
            if (ni >= 2)
            {
                if (ret.ContainsKey(ni))
                    ret[ni] += 1;
                else ret[ni] = 1;
            }
        }
        return ret;
    }
    public static List<long> DivisorEnumrate(long N)
    {
        var ret = new List<long>();
        for (long i = 1; i * i <= N; ++i)
        {
            if (N % i == 0)
            {
                ret.Add(i);
                ret.Add(N / i);
            }
        }
        return ret;
    }
    public static List<int> seive(int n)
    {
        var ret = new List<int>();
        bool[] isPrime = new bool[n + 1];
        for (int i = 1; i <= n; ++i) isPrime[i] = true;
        isPrime[1] = false;
        for (int i = 1; i <= n; ++i)
        {
            int j = i;
            if (isPrime[i]) ret.Add(i);
            else continue;
            while (j <= n)
            {
                j += i;
                if (j > n) continue;
                isPrime[j] = false;
            }
        }
        return ret;
    }
    public static bool isPrime(long n)
    {
        for (int i = 2; i * i <= n; ++i)
        {
            if (n % i == 0) return false;
        }
        return true;
    }
}
public class BinarySearch
{
    public static int Lower_Bound<T>(IList<T> Array, T Target)
    {
        return Lower_Bound<T>(Array, Target, Comparer<T>.Default.Compare);
    }
    public static int Lower_Bound<T>(IList<T> Array, T Target, Comparison<T> Comp)
    {
        var cmp = Comparer<T>.Create(Comp);
        var l = -1; //always ng
        var r = Array.Count(); //always ok
        while (r - l > 1)
        {
            var mid = l + (r - l) / 2;
            var res = cmp.Compare(Array[mid], Target);
            if (res >= 0) r = mid;
            else l = mid;
        }
        return r;
    }
    public static int Upper_Bound<T>(IList<T> Array, T Target)
    {
        return Upper_Bound<T>(Array, Target, Comparer<T>.Default.Compare);
    }
    public static int Upper_Bound<T>(IList<T> Array, T Target, Comparison<T> Comp)
    {
        var cmp = Comparer<T>.Create(Comp);
        var l = -1;
        var r = Array.Count;
        while (r - l > 1)
        {
            var mid = l + (r - l) / 2;
            var res = cmp.Compare(Array[mid], Target);
            if (res > 0) r = mid;
            else l = mid;
        }
        return r;
    }
}
public static class Math2
{
    public const int INF = 1 << 29;
    public const long INFL = 1L << 60;
    public const long MOD = 1000000007;
    public const long MOD2 = 998244353;

    public static long Power(long a, long b, long MOD = 1000000007) //i^N
    {
        long res = 1;
        while (b > 0)
        {
            if ((b & 1) != 0) res = res * a % MOD;
            a = a * a % MOD;
            b >>= 1;
        }
        return res;
    }
    public static long Power2(long a, long b) //i^N
    {
        long res = 1;
        while (b > 0)
        {
            if ((b & 1) != 0) res = res * a;
            a = a * a;
            b >>= 1;
        }
        return res;
    }
    public static long GCD(long a, long b)
    {
        if (a == 0) return b;
        while (b > 0)
        {
            var r = a % b;
            a = b;
            b = r;
        }
        return a;
    }
    public static long LCM(long a, long b) => (b / GCD(a, b)) * a;
    public static long Comb(long n, long r, int MOD = 1000000007)
    {
        if (r > n - r) r = n - r;
        long Nume = 1;
        long Deno = 1;

        if (r > n - r) r = n - r;
        for (long i = 1; i <= r; ++i)
        {
            Deno = (Deno * i) % MOD;
            Nume = Nume * (n - i + 1) % MOD;
        }
        return (Nume * inv(Deno)) % MOD;
    }
    public static long Comb2(long n, long r)
    {
        long Nume = 1;
        long Deno = 1;

        if (r > n - r) r = n - r;
        for (long i = 1; i <= r; ++i)
        {
            Deno *= i;
            Nume *= n - i + 1;
        }
        return Nume / Deno;
    }
    public static long inv(long x, int MOD = 1000000007)
    {
        return Power(x, MOD - 2, MOD);
    }
}
public static class Utils
{
    public static void Swap<T>(ref T A, ref T B)
    {
        T x = A;
        A = B;
        B = x;
    }
    public static int DigitSum(string N)
    {

        int ret = 0;
        for (int i = 0; i < N.Length; ++i) ret += N[i] - '0';
        return ret;
    }
    public static string ConvertBase(long N, int K)
    {
        StringBuilder ret = new StringBuilder();
        while (N > 0)
        {
            var r = N % K;
            N /= K;
            ret.Append(r);
        }
        return new string(ret.ToString().ToCharArray().Reverse().ToArray());
    }
    public static bool NextPermutation<T>(IList<T> lis, Comparison<T> cmp)
    {
        int n = lis.Count;
        int i = n - 1;
        while (i - 1 >= 0)
        {
            if (cmp(lis[i - 1], lis[i]) < 0) break;
            --i;
        }
        if (i == 0) return false;
        int j = i;
        while (j + 1 < n)
        {
            if (cmp(lis[i - 1], lis[j + 1]) > 0) break;
            ++j;
        }
        var _q = lis[j];
        lis[j] = lis[i - 1];
        lis[i - 1] = _q;
        int k = i;
        int l = n - 1;
        while (k < l)
        {
            var _p = lis[k];
            lis[k] = lis[l];
            lis[l] = _p;

            ++k;
            --l;
        }
        return true;
    }
    public static bool NextPermutation<T>(IList<T> lis) => NextPermutation(lis, Comparer<T>.Default.Compare);
}
public class PriorityQueue<T>
{
    List<T> _item;
    public int Count { get { return _item.Count; } }
    bool _isascend { get; set; }
    public T Peek { get { return _item[0]; } }
    Comparison<T> Comp;
    public PriorityQueue(bool IsAscend = true, IEnumerable<T> list = null) : this(Comparer<T>.Default.Compare, IsAscend, list) { }
    public PriorityQueue(Comparison<T> cmp, bool IsAscend = true, IEnumerable<T> list = null)
    {
        _item = new List<T>();
        _isascend = IsAscend;
        this.Comp = cmp;
        if (list != null)
        {
            _item.AddRange(list);
            Build();
        }
    }

    private int Compare(int i, int j) => (_isascend ? -1 : 1) * Comp(_item[i], _item[j]);
    private void Swap(int i, int j) { var t = _item[i]; _item[i] = _item[j]; _item[j] = t; }
    private int Parent(int i) => (i - 1) >> 1;
    private int Left(int i) => (i << 1) + 1;
    public T Enqueue(T val)
    {
        int i = _item.Count;
        _item.Add(val);
        while (i > 0)
        {
            int p = Parent(i);
            if (Compare(i, p) > 0)
                Swap(i, p);
            i = p;
        }
        return val;
    }
    private void Heapify(int index)
    {
        for (int i = index, j;
            (j = Left(i)) < _item.Count; i = j)
        {
            if (j != _item.Count - 1 && Compare(j, j + 1) < 0) j++;
            if (Compare(i, j) < 0)
                Swap(i, j);
        }
    }
    public T Dequeue()
    {
        T val = _item[0];
        _item[0] = _item[_item.Count - 1];
        _item.RemoveAt(_item.Count - 1);
        Heapify(0);
        return val;
    }
    private void Build()
    {
        for (var i = (_item.Count >> 1) - 1; i >= 0; i--)
            Heapify(i);
    }
    public bool Any() => Count > 0;
}
class Program
{
    static void Main(string[] args)
    {
        var CP = new CP();
        CP.Solve();
    }
}
public static class Output
{

    public static void Put(string a) => Console.WriteLine(a);
    public static void Put(params object[] i) => Put(string.Join(" ", i));
    public static void Put<T>(IEnumerable<T> a) => Put(string.Join(" ", a));
    public static void PutV<T>(IEnumerable<T> a) { foreach (var z in a) Put(z); }
    public static void YN(bool i)
    {
        if (i) Put("Yes");
        else Put("No");
    }
}
public class Input
{
    public static string Str => Console.ReadLine();
    public static bool IsTypeEqual<T, U>() => typeof(T).Equals(typeof(U));
    public static T ConvertType<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    public static T Cast<T>(string s)
    {
        if (IsTypeEqual<T, int>()) return ConvertType<T, int>(int.Parse(s));
        else if (IsTypeEqual<T, long>()) return ConvertType<T, long>(long.Parse(s));
        else if (IsTypeEqual<T, double>()) return ConvertType<T, double>(double.Parse(s));
        else if (IsTypeEqual<T, char>()) return ConvertType<T, char>(char.Parse(s));
        else return ConvertType<T, string>(s);
    }
    public static T[] Castarr<T>(string[] s)
    {

        var ret = new T[s.Length];
        int i = 0;
        if (IsTypeEqual<T, char>())
        {
            var list = new List<T>();
            foreach (var t in s)
            {
                foreach (var u in t)
                {
                    list.Add(ConvertType<T, char>(char.Parse(u.ToString())));
                }
            }
            return list.ToArray();
        }
        foreach (var t in s)
        {
            if (IsTypeEqual<T, int>()) ret[i++] = ConvertType<T, int>(int.Parse(t));
            else if (IsTypeEqual<T, long>()) ret[i++] = ConvertType<T, long>(long.Parse(t));
            else if (IsTypeEqual<T, double>()) ret[i++] = ConvertType<T, double>(double.Parse(t));
            else ret[i++] = ConvertType<T, string>(t);
        }
        return ret;
    }
    Queue<string> q = new Queue<string>();
    void next() { var ss = Str.Split(' '); foreach (var item in ss) q.Enqueue(item); }
    public T cin<T>() { if (!q.Any()) next(); return Cast<T>(q.Dequeue()); }
    public void mul<T>(out T t) { t = cin<T>(); }
    public void mul<T, U>(out T t, out U u) { t = cin<T>(); u = cin<U>(); }
    public void mul<T, U, V>(out T t, out U u, out V v) { t = cin<T>(); u = cin<U>(); v = cin<V>(); }
    public void mul<T, U, V, W>(out T t, out U u, out V v, out W w) { t = cin<T>(); u = cin<U>(); v = cin<V>(); w = cin<W>(); }
    public void mul<T, U, V, W, X>(out T t, out U u, out V v, out W w, out X x) { t = cin<T>(); u = cin<U>(); v = cin<V>(); w = cin<W>(); x = cin<X>(); }
    public void mul<T, U, V, W, X, Y>(out T t, out U u, out V v, out W w, out X x, out Y y) { t = cin<T>(); u = cin<U>(); v = cin<V>(); w = cin<W>(); x = cin<X>(); y = cin<Y>(); }
    public void mul<T, U, V, W, X, Y, Z>(out T t, out U u, out V v, out W w, out X x, out Y y, out Z z) { t = cin<T>(); u = cin<U>(); v = cin<V>(); w = cin<W>(); x = cin<X>(); y = cin<Y>(); z = cin<Z>(); }
    public T[] cinarr<T>() { return Castarr<T>(Str.Split(' ')); }
}