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: Wrong Answer)

//#include <iostream>
//#include <string>
//#include <stdlib.h>
#include <stdio.h>

int main() {
    int N;
    scanf("%d", &N);
    int a[N];
    int b[N];
    int x[N];
    for (int i = 0; i < N; i++) {
        scanf("%d", &a[i]);
    }
    for (int i = 0; i < N; i++) {
        scanf("%d", &b[i]);
    }
    for (int i = 0; i < N; i++) {
        x[i] = a[i] - b[i];
    }
    int ca = 0;
    int cb = 0;
    for (int i = 0; i < N; i++) {
        if (x[i] > 0) {
            cb += x[i];
        } else if (x[i] < 0) {
            if (x[i] % 2 == 0) {
                ca -= x[i] / 2;
            } else {
                ca -= (x[i] - 1) / 2;
                cb += 1;
            }
        }
    }
    if ((2*ca - cb >= ca || 2*ca - cb >= cb) && !(2*ca - cb == ca && 2*ca - cb == ca)) {
        printf("%s\n", "Yes");
    } else {
        printf("%s\n", "No");
    }
    return 0;
}