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<cstdio>  
#include<cstring>  
#include<algorithm>  
#include<iostream>  
#include<string>  
#include<vector>  
#include<stack>  
#include<bitset>  
#include<cstdlib>  
#include<cmath>  
#include<set>  
#include<list>  
#include<deque>  
#include<map>  
#include<queue>
using namespace std;
typedef long long ll;
const ll inf=1<<29;
const ll Maxn=1e6;

int a[Maxn],b[Maxn];

int main(){
	int n;
	int sum1=0,sum2=0,s=0,t=0,w=0,p=0;
	cin>>n;
	for(int i=1;i<=n;i++){
		scanf("%d",&a[i]);
		sum1+=a[i];
	}
	for(int i=1;i<=n;i++){
		scanf("%d",&b[i]);
		sum2+=b[i];
	}
	if(sum1>sum2) printf("No\n");
	if(sum1<sum2){
		for(int i=1;i<=n;i++){
			if(a[i]>b[i]) s++;
			if(a[i]<b[i]) t++;
			if(a[i]%2==1) w++;
			if(b[i]%2==0) p++;
		}
		if(s==t&&w==p) printf("Yes\n");
		else printf("No\n");
	}
	if(sum1==sum2){
		int ans=0;
		sort(a+1,a+1+n);
		sort(b+1,b+1+n);
		for(int i=1;i<=n;i++){
			if(a[i]==b[i]) ans++;
		}
		if(ans==n) printf("Yes\n");
		else printf("No\n");
	}
}