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 Rust (1.15.1) (judge verdict: Wrong Answer)

use std::io::stdin;

fn main() {
    let mut st = String::new();
    stdin().read_line(&mut st).unwrap();
    let n = st.trim().parse::<usize>().unwrap();
    let mut st = String::new();
    stdin().read_line(&mut st).unwrap();
    let a:Vec<_> = st.trim().split(" ").map(|x| x.parse::<i64>().unwrap()).collect();
    let mut st = String::new();
    stdin().read_line(&mut st).unwrap();
    let b:Vec<_> = st.trim().split(" ").map(|x| x.parse::<i64>().unwrap()).collect();
    let mut x:i64 = 0;
    let mut y:i64 = 0;
    let mut c:i64 = 0;
    for i in 0..n {
        c += b[i] - a[i];
        if b[i] < a[i] {
            x += a[i]-b[i];
        } else {
            y += (b[i]-a[i])/2;
        };
    };

    if c >= y+x {
        println!("Yes");
    } else {
        println!("No");
    }
}