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: Time Limit Exceeded)

extern crate core;

use std::io::{self, Read};

fn main() {
    let mut input = String::new();
    io::stdin().read_to_string(&mut input).unwrap();
    let output = run(input.trim().to_string());
    println!("{}", output);
}

fn run(input: String) -> String {
    let list = input
        .split("\n")
        .skip(1)
        .map(|x| {
            x.split_whitespace()
                .map(|x| x.parse::<i64>().unwrap())
                .collect::<Vec<_>>()
        })
        .collect::<Vec<_>>();

    let mut a = list[0].clone();
    let mut b = list[1].clone();

    let mut a_sum = a.iter().sum::<i64>();
    let mut b_sum = b.iter().sum::<i64>();

    loop {
        if a == b {
            return "Yes".to_string();
        }
        if a_sum >= b_sum {
            return "No".to_string();
        }

        let mut is_a = false;
        let mut is_b = false;
        for i in 0..a.len() {
            if !is_a && a[i] < b[i] {
                a[i] += 2;
                a_sum += 2;
                is_a = true;
            }

            if !is_b && b[i] < a[i] {
                b[i] += 1;
                b_sum += 1;
                is_b = true;
            }

            if is_a && is_b {
                break;
            }
        }
    }
}

#[test]
fn test() {
    let tests = vec![
        (
            "3
1 2 3
5 2 2",
            "Yes",
        ),
        (
            "5
3 1 4 1 5
2 7 1 8 2",
            "No",
        ),
        (
            "5
2 7 1 8 2
3 1 4 1 5",
            "No",
        ),
    ];
    for (i, (input, output)) in tests.into_iter().enumerate() {
        println!("test:{}", i);
        assert_eq!(run(input.to_string()), output.to_string());
    }
}