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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;

public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		int n = Integer.parseInt(br.readLine());

		String str[] = br.readLine().split(" ");

		long a[] = new long[n];

		for (int i = 0; i < n; i++) {
			a[i] = Long.parseLong(str[i]);
		}

		long s[] = new long[n + 1];
		s[0] = a[0];

		for (int i = 0; i < n - 1; i++) {
			s[i + 1] = s[i] + a[i + 1];
		}

		Arrays.sort(s);

		Map<Long, Long> map = new HashMap<>();

		for (int i = 0; i < n; i++) {
			if (map.containsKey(s[i])) {
				map.put(s[i], map.get(s[i]) + 1);
			} else {
				map.put(s[i], 1L);
			}
		}

		long ans = 0;

		int m = 1;
		for (int i = 0; i < n; i++) {
			if (s[i] == s[i + 1]) {
				m++;
			} else {
				m = 1;
			}
			ans += m - 1;
		}

		System.out.println(ans);
	}
}