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: Time Limit Exceeded)

using System;
using System.Linq;

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

			for (int l_iIndex = 0; l_iIndex < l_aiInput1.Length; l_iIndex++)
			{
				while (l_aiInput1[l_iIndex] > l_aiInput2[l_iIndex])
				{
					for (int l_iIndex2 = 0; l_iIndex2 < l_aiInput1.Length; l_iIndex2++)
					{
						if (l_aiInput1[l_iIndex2] + 1 < l_aiInput2[l_iIndex2])
						{
							l_aiInput2[l_iIndex]++;
							l_aiInput1[l_iIndex2] += 2;
							goto Do_Continue;
						}
					}
					Console.WriteLine("No");
					return;

					Do_Continue:;
				}
			}
			Console.WriteLine("Yes");

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