Problem:
Score : 300 points

Problem Statement

You are given two integer sequences of length N: a_1,a_2,..,a_N and b_1,b_2,..,b_N.
Determine if we can repeat the following operation zero or more times so that the sequences a and b become equal.

Operation: Choose two integers i and j (possibly the same) between 1 and N (inclusive), then perform the following two actions simultaneously:

Add 2 to a_i.

Add 1 to b_j.

Constraints

1 ≤ N ≤ 10 000

0 ≤ a_i,b_i ≤ 10^9 (1 ≤ i ≤ N)

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 .. a_N
b_1 b_2 .. b_N

Output

If we can repeat the operation zero or more times so that the sequences a and b become equal, print Yes; otherwise, print No.

Sample Input 1

3
1 2 3
5 2 2

Sample Output 1

Yes

For example, we can perform three operations as follows to do our job:

First operation: i=1 and j=2. Now we have a = \{3,2,3\}, b = \{5,3,2\}.

Second operation: i=1 and j=2. Now we have a = \{5,2,3\}, b = \{5,4,2\}.

Third operation: i=2 and j=3. Now we have a = \{5,4,3\}, b = \{5,4,3\}.

Sample Input 2

5
3 1 4 1 5
2 7 1 8 2

Sample Output 2

No

Sample Input 3

5
2 7 1 8 2
3 1 4 1 5

Sample Output 3

No

Solution in C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
class Program
 {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            string[] strListA = Console.ReadLine().Split(' ');
            string[] strListB = Console.ReadLine().Split(' ');
            int[] listA = new int[N];
            int[] listB = new int[N];
            for(int i = 0; i < N; i++){
                listA[i] = int.Parse(strListA[i]);
                listB[i] = int.Parse(strListB[i]);
            }
            bool flag = true;
            int number = 0;
            bool[] equalMemo = new bool[N];
            while(number < N){
                if(listA[number] >= listB[number]){
                    number++;
                    equalMemo[number] = false;
                } else if(listA[number] == listB[number]){
                    number++;
                    equalMemo[number] = true;
                } else {
                    listA[number] += 2;
                    int numB = 0;
                    bool numBFlag = true;
                    while(numBFlag && numB < number){
                        if(!equalMemo[numB]){
                            listB[numB]++;
                            numBFlag = false;
                            if(listA[numB] == listB[numB]){
                                equalMemo[numB] = true;
                            }
                        }
                        numB++;
                    }
                    if(numBFlag){
                        listB[number]++;
                    }
                }
            }
            bool answer = true;
            for(int i = 0; i < N; i++){
                if(!equalMemo[i]){
                    answer = false;
                }
            }
            // Console.Write("改行なし a = {0} b = {1} c = {2}", a, b, c)//改行なし出力
            // Console.WriteLine("改行あり a = {0} b = {1} c = {2}", a, b, c);//改行付き出力
            if(answer){
                Console.WriteLine("Yes");
            } else {
                Console.WriteLine("No");
            }
        }
 }