Problem: Jafar has n cans of cola. Each can is described by two integers: remaining volume of cola ai and can's capacity bi (ai ≤  bi).

Jafar has decided to pour all remaining cola into just 2 cans, determine if he can do this or not!

Input

The first line of the input contains one integer n (2 ≤ n ≤ 100 000) — number of cola cans.

The second line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 109) — volume of remaining cola in cans.

The third line contains n space-separated integers that b1, b2, ..., bn (ai ≤ bi ≤ 109) — capacities of the cans.

Output

Print "YES" (without quotes) if it is possible to pour all remaining cola in 2 cans. Otherwise print "NO" (without quotes).

You can print each letter in any case (upper or lower).

Examples

Input

2
3 5
3 6


Output

YES


Input

3
6 8 9
6 10 12


Output

NO


Input

5
0 0 5 0 0
1 1 8 10 5


Output

YES


Input

4
4 1 0 3
5 2 2 3


Output

YES

Note

In the first sample, there are already 2 cans, so the answer is "YES".

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

import static java.lang.Math.*;

public class Solution {

    BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter out = new PrintWriter(System.out);
    StringTokenizer tok = new StringTokenizer("");

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    int gcd(int a, int b) {
        if (b == 0) return a;
        else return gcd(b, a % b);
    }

    void solveT() throws IOException {
        int n = readInt();
        long sum = 0;
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            sum += readInt();
        }
        
        for (int i = 0; i < n; i++) {
            a[i] = readInt();
        }
        
        Arrays.sort(a);
        if (a[n - 1] + a[n - 2] >= sum) {
            out.print("YES");
        } else {
            out.print("NO");
        }
    }

    void solve() throws IOException {
        int n = 1;
        for (int i = 0; i < n; i++) {
            solveT();
        }
    }


    void run() throws IOException {
        solve();
        out.flush();
    }

    public static void main(String[] args) throws IOException {
        new Solution().run();
    }
}