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<vector>
#include<cstring>
#include<algorithm>
#include<math.h>
#include<queue>
#include<deque>
#include<map>
#include<bitset>

#define rep(i, n) for(int i = 0;i < (n);i++)
#define repr(i, n) for(int i = (n);i >= 0;i--)
#define repf(i, m, n) for(int i = (m);i < (n);i++)

using namespace std;
using ll = long long;

template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1;} return 0;}
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1;} return 0;}

int dx[] = {0, 1, 0, -1}, dy[] = {1, 0, -1, 0};


//////////////////////////////////////////////////



int main() {
    int n; cin >> n;
    vector<int> a(n), b(n);
    for (int i = 0; i < n; i++)
    {
        cin >> a[i];
    }
    for (int i = 0; i < n; i++)
    {
        cin >> b[i];
    }
    

    vector<int> ab(2);
    for (int i = 0; i < n; i++)
    {
        if (a[i] > b[i]) {
            ab[1] += a[i]-b[i];
        } else if (a[i] < b[i]){
            if ((b[i]-a[i])%2 == 0) {
                ab[0] += (b[i]-a[i])/2;
            } else {
                ab[0] += (b[i]-a[i]+1)/2;
                ab[1] -= 1;
            }
        }
        // cout << ab[0] << ' ' << ab[1] << endl;
    }
    
    // cout << ab[0] << ' ' << ab[1] << endl;

    if ((ab[1]*2) == ab[0]) {
        cout << "Yes" << endl;
    } else {
        cout << "No" << endl;
    }
    
    return 0;
}