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: Accepted)

#include<bits/stdc++.h>
using namespace std;


int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	
	int N; cin >> N;
	long long a[11000], b[11000];
	for (int i = 0; i < N; i++) {
		cin >> a[i];
	}
	long long suma = 0, sumb = 0;
	for (int i = 0; i < N; i++) {
		cin >> b[i];
	}
	for (int i = 0; i < N; i++) {
		long long d = a[i] - b[i];
		if (d < 0) {
			if (d % 2 == 0)suma += -d;
			else {
				suma += -d + 1;
				sumb++;
			}
		}
		else if (d > 0) {
			sumb += d;
		}

	}
	if (suma >= sumb * 2)cout << "Yes";
	else cout << "No";
}