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;
using System.Linq;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] a_asArgs)
        {
			Console.ReadLine();
			int[] l_aiInput1 = Console.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();
			int[] l_aiInput2 = Console.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();

			int l_iSum1 = l_aiInput1.Sum();
			int l_iSum2 = l_aiInput2.Sum();

			int l_iTurnMax = l_iSum2 - l_iSum1;
			int l_iTurn = 0;
			for (int l_iIndex = 0; l_iIndex < l_aiInput1.Length; l_iIndex++)
			{
				if (l_aiInput1[l_iIndex] > l_aiInput2[l_iIndex])
				{
					l_iTurn += l_aiInput1[l_iIndex] - l_aiInput2[l_iIndex];
				}
				else if (l_aiInput1[l_iIndex] < l_aiInput2[l_iIndex])
				{
					l_iTurn += (l_aiInput2[l_iIndex] - l_aiInput1[l_iIndex]) / 2;
				}
			}
			Console.WriteLine((l_iTurn <= l_iTurnMax) ? "Yes" : "No");

			/* このアプローチのどこに問題があったのかを調べたい。
			int l_iLarge1 = 0;
			int l_iLarge2 = 0;

			for (int l_iIndex = 0; l_iIndex < l_aiInput1.Length; l_iIndex++)
			{
				if (l_aiInput1[l_iIndex] > l_aiInput2[l_iIndex])
				{
					l_iLarge1 += l_aiInput1[l_iIndex] - l_aiInput2[l_iIndex];
				}
				else if (l_aiInput1[l_iIndex] < l_aiInput2[l_iIndex])
				{
					l_iLarge2 += (l_aiInput2[l_iIndex] - l_aiInput1[l_iIndex]) / 2 * 2;
				}
			}
			Console.WriteLine((l_iLarge1 * 2 <= l_iLarge2) ? "Yes" : "No");
			*/
		}
	}
}