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: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using static System.Math;

namespace CSharpSpiral {
	class Program {
		static void Main(string[] args) {
			var sw = new StreamWriter(Console.OpenStandardOutput()) {
				AutoFlush=
#if DEBUG
			true
#else
			false
#endif
			};
			Console.SetOut(sw);
			new Program().Solve(new ConsoleInput(
#if DEBUG
			new StreamReader("../../../inputData.txt")
#else
			Console.In
#endif
			, ' '));
			Console.Out.Flush();
		}
		public void Solve(ConsoleInput cin) {
			var N = cin.ReadInt;
			var TK = cin.ReadIntArray(N);
			var AO = cin.ReadIntArray(N);
			var psbl = new long[N];
			psbl[0]=psbl[N-1]=1;
			if(N==1&&TK[0]!=AO[0]) {
				Console.WriteLine(0); return;
			} else if(N>1&&
					(AO[0]!=TK[N-1]
						||AO[0]!=AO[1]&&AO[0]!=TK[0]
						||TK[N-1]!=TK[N-2]&&TK[N-1]!=AO[N-1]
					)
				) {
				Console.WriteLine(0); return;
			}
			for(int i = 1; i<N-1; i++) {
				var tt = TK[i]!=TK[i-1];
				var aa = AO[i]!=AO[i+1];
				if(!tt&&!aa) {
					psbl[i]=Min(TK[i], AO[i]);
					continue;
				}
				if(tt) {
					//AO[i]==Max(AO[i+1],TK[i])
					if(aa) {
						if(TK[i]!=AO[i]) {
							Console.WriteLine(0); return;
						}
					} else {
						if(TK[i]>AO[i]) {
							Console.WriteLine(0); return;
						}
					}
				} else if(aa) {
					if(AO[i]>TK[i]) {
						Console.WriteLine(0); return;
					}
				}
				psbl[i]=1;
			}
			var F = new QuotientRing();
			var Res = 1L;
			for(int i = 0; i<N; i++) {
				Res=F.Mul(Res, psbl[i]);
			}
			Console.WriteLine(Res);
		}
	}
	class QuotientRing {
		public readonly long modulo;
		public QuotientRing(int mModulo = 1000*1000*1000+7) {
			modulo=mModulo;
		}
		private long[] factorialTable = { 1 };
		private int factorialTableLastIndex { get { return factorialTable.Length-1; } }
		public long mod(long x) => x<0 ? x%modulo+modulo : x%modulo;
		public long Add(long a, long b) => mod(a+b);
		public long Sub(long a, long b) => mod(a-b);
		public long Mul(long a, long b) => mod(a*b);
		public long Pow(long a, long n) {
			if(n==0) return 1;
			var R = 1L;
			n=n<0 ? n%(modulo-1)+(modulo-1) : n%(modulo-1);
			for(; n>0; a=Mul(a, a), n>>=1) {
				if((n&1)!=0) R=Mul(R, a);
			}
			return R;
		}
		private void ExpandFactorialTable(int N) {
			var k = factorialTableLastIndex;
			Array.Resize(ref factorialTable, N+1);
			for(int i = k+1; i<=N; i++) {
				if(i==0) { factorialTable[i]=1; continue; }
				factorialTable[i]=Mul(factorialTable[i-1], i);
			}
		}
		public long Factorial(int n) {
			if(n>factorialTableLastIndex)
				ExpandFactorialTable(n);
			return factorialTable[n];
		}
		public long Permutation(int n, int k) {
			if(k<0||k>n) return 0;
			var Res = 1L;
			for(int i = 0; i<k; i++)
				Res=Mul(Res, n-i);
			return Res;
		}
		public virtual long Calculate(params object[] RPN) {
			var S = new Stack<long>();
			foreach(var token in RPN) {
				var type = token.GetType();
				if(type==typeof(int)||type==typeof(long)) {
					S.Push((long)token);
				} else if(type==typeof(char)) {
					long v1 = 0L, v2 = 0L;
					v2=S.Pop();
					HashSet<char> unaries = new HashSet<char>() { '!' };
					if(!unaries.Contains((char)token))
						v1=S.Pop();
					long res;
					switch((char)token) {
						case '+': res=Add(v1, v2); break;
						case '-': res=Sub(v1, v2); break;
						case '*': res=Mul(v1, v2); break;
						case '^': res=Pow(v1, v2); break;
						case '!': res=Factorial((int)v2); break;
						default: throw new InvalidOperationException();
					}
					S.Push(res);
				} else throw new InvalidOperationException();
			}
			return S.Peek();
		}
	}
	static class ExtendClass {
		public static string Join<T>(this IEnumerable<T> X, string separator = " ") => string.Join(separator, X);
	}
	class ConsoleInput {
		private readonly TextReader _stream;
		private readonly char _separator = ' ';
		private readonly Queue<string> inputStream;
		public ConsoleInput(TextReader stream, char separator = ' ') {
			this._separator=separator;
			this._stream=stream;
			inputStream=new Queue<string>();
		}
		public string Read {
			get {
				if(inputStream.Count!=0) return inputStream.Dequeue();
				string[] tmp = _stream.ReadLine().Split(_separator);
				for(int i = 0; i<tmp.Length; ++i)
					inputStream.Enqueue(tmp[i]);
				return inputStream.Dequeue();
			}
		}
		public string ReadLine { get { return _stream.ReadLine(); } }
		public int ReadInt { get { return int.Parse(Read); } }
		public long ReadLong { get { return long.Parse(Read); } }
		public double ReadDouble { get { return double.Parse(Read); } }
		public string[] ReadStrArray(long N) {
			var ret = new string[N];
			for(long i = 0; i<N; ++i)
				ret[i]=Read;
			return ret;
		}
		public int[] ReadIntArray(long N) { var ret = new int[N]; for(long i = 0; i<N; ++i) ret[i]=ReadInt; return ret; }
		public long[] ReadLongArray(long N) { var ret = new long[N]; for(long i = 0; i<N; ++i) ret[i]=ReadLong; return ret; }
		public double[] ReadDoubleArray(long N) { var ret = new double[N]; for(long i = 0; i<N; ++i) ret[i]=ReadDouble; return ret; }
		public bool isEOF {
			get { return _stream.Peek()==-1; }
		}
	}

}