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`.

Examples

Input

3
1 2 3
5 2 2


Output

Yes


Input

5
3 1 4 1 5
2 7 1 8 2


Output

No


Input

5
2 7 1 8 2
3 1 4 1 5


Output

No
import java.util.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws IOException {
        InputReader in = new InputReader();
        PrintWriter out = new PrintWriter(System.out);
        Solver s = new Solver();
        int test = 1;
        for (int i = 1; i <= test; i++) {
            s.solve(i, in, out);
        }
        out.close();
    }
}

class Solver {

    void solve(int test_case, InputReader in, PrintWriter out) throws IOException {
        int n = in.nextInt();
        int[] a = new int[n];
        int[] b = new int[n];
        for (int i = 0; i < n; i++) a[i] = in.nextInt();
        for (int i = 0; i < n; i++) b[i] = in.nextInt();
        long a1 = 0, b1 = 0;
        for (int i = 0; i < n; i++) {
            if (a[i] < b[i]) {
                b1 += (b[i] - a[i]) / 2;
            }
        }
//        out.println(b1);
        for (int i = 0; i < n; i++) {
            if (a[i] > b[i]) {
//                out.println(b1 + " " + (a[i] - b[i]));
                if (b1 - (a[i] - b[i]) < 0) {
                    out.println("No");
                    return;
                } else {
                    b1 -= (a[i] - b[i]);
                }
            }
        }
        out.println("Yes");
    }
}


class InputReader {
    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public InputReader() {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public InputReader(String file_name) throws IOException {
        din = new DataInputStream(new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public String nextLine() throws IOException {
        byte[] buf = new byte[64]; // line length
        int cnt = 0, c;
        while ((c = read()) != -1) {
            if (c == '\n')
                break;
            buf[cnt++] = (byte) c;
        }
        return new String(buf, 0, cnt);
    }

    public int nextInt() throws IOException {
        int ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');

        if (neg)
            return -ret;
        return ret;
    }

    public long nextLong() throws IOException {
        long ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        }
        while ((c = read()) >= '0' && c <= '9');
        if (neg)
            return -ret;
        return ret;
    }

    public double nextDouble() throws IOException {
        double ret = 0, div = 1;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();

        do {
            ret = ret * 10 + c - '0';
        }
        while ((c = read()) >= '0' && c <= '9');

        if (c == '.') {
            while ((c = read()) >= '0' && c <= '9') {
                ret += (c - '0') / (div *= 10);
            }
        }

        if (neg)
            return -ret;
        return ret;
    }

    private void fillBuffer() throws IOException {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1)
            buffer[0] = -1;
    }

    private byte read() throws IOException {
        if (bufferPointer == bytesRead)
            fillBuffer();
        return buffer[bufferPointer++];
    }

    public void close() throws IOException {
        if (din == null)
            return;
        din.close();
    }

    public String next() throws IOException {
        byte[] buf = new byte[64]; // line length
        int cnt = 0, c;
        while ((c = read()) != -1) {
            if (c == '\n' || c == ' ')
                break;
            buf[cnt++] = (byte) c;
        }
        return new String(buf, 0, cnt);
    }
}