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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define rep(i,N) for(ll (i)=0;(i)<(N);(i)++)
#define chmax(x,y) x=max(x,y)
#define chmin(x,y) x=min(x,y)
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
const int mod = 1000000007;
const int INF = 1001001001;

int main() {
  int n;
  cin >> n;
  vector<int> a(n), b(n);
  rep(i, n) cin >> a[i] >> b[i];
  sort(a.begin(), a.end());
  sort(b.begin(), b.end());
  int suma = 0;
  int sumb = 0;
  rep(i, n) suma += a[i];
  rep(i, n) sumb += b[i];
  int costa = 0;
  int costb = 0;
  rep(i, n) {
    if (a[i] < b[i]) {
      int num = (b[i] - a[i] + 1) / 2;
      costa += num;
      if (a[i] != b[i]) costb++;
    } else {
      int num = a[i] - b[i];
      costb += num;
    }
  }
  if (costa != costb) cout << "No" << endl;
  else cout << "Yes" << endl;
}