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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace apc001b
{
    public class TwoArrays
    {
        List<int> a_, b_;

        public TwoArrays(string a, string b) {
            a_ = a.Split().ToList().ConvertAll(int.Parse);
            b_ = b.Split().ToList().ConvertAll(int.Parse);
        }

        private int Determine_i() {
            var maxDiffColumnNumber = 0;
            var maxDiff = b_[maxDiffColumnNumber] - a_[maxDiffColumnNumber]; ;
            for(var i = 1; i < a_.Count(); ++i) {
                var diff = b_[i] - a_[i];
                if(maxDiff < diff) {
                    maxDiff = diff;
                    maxDiffColumnNumber = i;
                }
            }
            return maxDiffColumnNumber;
        }

        private int Determine_j() {
            var minDiffColumnNumber = 0;
            var minDiff = b_[minDiffColumnNumber] - a_[minDiffColumnNumber];
            for(var j = 1; j < a_.Count(); ++j) {
                var diff = b_[j] - a_[j];
                if(diff < minDiff) {
                    minDiff = diff;
                    minDiffColumnNumber = j;
                }
            }
            return minDiffColumnNumber;
        }

        private bool AreTwoArraysSame() {
            return a_.SequenceEqual(b_);
        }

        private void IncrementTwoArrays() {
            a_[Determine_i()] += 2;
            b_[Determine_j()]++;
        }

        public string Solve() {
            const int maxNumberOfTry = 10000;
            var numberOfTry = 0;
            var isAvailable = false;
            while(numberOfTry < maxNumberOfTry) {
                if(AreTwoArraysSame()) {
                    isAvailable = true;
                    break;
                } else {
                    IncrementTwoArrays();
                    ++numberOfTry;
                }
            }
            return isAvailable ? "Yes" : "No";
        }
    }

    class Apc001b
    {
        static void Main(string[] args) {
            Console.ReadLine();
            var a = Console.ReadLine();
            var b = Console.ReadLine();
            var arrays = new TwoArrays(a, b);
            Console.WriteLine(arrays.Solve());
        }
    }
}