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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <vector>
using namespace std;
int N;
int Check(vector<int> &A,vector<int> &B)
{
	int retGT=0;
	for (int i=0;i<N;i++){
		if (A[i]<B[i]){
			return -1;
		}else if (A[i]>B[i]){
			retGT=1;
		}
	}
	if (retGT==0){
		return 0;
	}else{
		return 1;
	}
	/*bool bOK=true;
	vector<int>::iterator vitA,vitB;
	for (vitA=A.begin(),vitB=B.begin();vitA!=A.end(),vitB!=B.end();vitA++,vitB++){
		if ((*vitA)==(*vitB)){
			A.erase(vitA);
			B.erase(vitB);
			vitA=A.begin();
			vitB=B.begin();
			N--;
		}else{
			return false;
		}
	}
	return bOK;
	*/
}
void getMinVId(vector<int> A,vector<int> B,int &minAId,int &minBId){
	int minA=A[0];
	int minB=B[0];
	int id=0;
	for (int i=0;i<N;i++){
		if (minA>A[i]){
			minA=A[i];
			minAId=i;
		}
		if (minB>B[i]){
			minB=B[i];
			minBId=i;
		}
	}
	return;
}			
int main(int argc, char* argv[])
{
	cin>>N;
	vector<int> A(N),B(N);
	vector<int> CA(N,0),CB(N,0);
	int i;
	for (i=0;i<N;i++){
		cin>>A[i];
	}
	for (i=0;i<N;i++){
		cin>>B[i];
	}
	if (Check(A,B)==0){
		cout<<"Yes"<<endl;
		return 0;
	}
	while(true){
		int minIdA=0,minIdB=0;
		getMinVId(A,B,minIdA,minIdB);
		A[minIdA]+=2;
		B[minIdB]+=1;
		int chk=Check(A,B);
		if (chk==0){
			cout<<"Yes"<<endl;
			return 0;
		}else if (chk==1){
			break;
		}
	}
	cout<<"No"<<endl;
	return 0;
}