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:
// https://codeforces.com/problemset/problem/892/A

import java.util.Scanner;
import java.util.Arrays;

public class chanchu {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt();

        long all = 0;

        if (a == 2) {
            System.out.println("YES");
            System.exit(0);
        }

        long A[] = new long[a];
        long B[] = new long[a];
        for (int i = 0; i < a; i++) {
            A[i] = sc.nextLong();
            all += A[i];
        }

        for (int i = 0; i < a; i++) {
            B[i] = sc.nextLong();
        }

        long max = B[0];
        int ind = 0;
        long s_max = B[0];
        int s_ind = 0;
        for (int i = 1; i < a; i++) {
            if (max < B[i]) {
                max = B[i];
                ind = i;
            }
        }

        for (int i = 0; i < a; i++) {
            if (ind != i && s_max < B[i]) {
                s_max = B[i];
                s_ind = i;
            }
        }
        
        long temp = all - A[ind] - A[s_ind];

        long temp_2 = (B[ind] - A[ind]) + (B[s_ind] - A[s_ind]);
        
        // System.out.println(max);
        // System.out.println(s_max);
        
        if (temp_2 >= temp) {
            System.out.println("YES");
        } else {
            System.out.println("NO");
        }

        // int ind = 0;
        // int val = 0;
        // long min = 100000000;
        // for (int i = 0; i < a; i++) {
        //     long b = B[i] - A[i];
        //     // System.out.println(b);
        //     // System.out.println(min != Math.min(min, b));

        //     if (min != Math.min(min, b)) {
        //         ind = i;
        //         min = Math.min(min, b);
        //     }
        // }
        
        // // System.out.println(ind);


        // // Arrays.sort(A);

        // for (int i = 0; i < a; i++) {
        //     if (ind == i) {
        //         continue;
        //     }
        //     long b = B[i] - A[i];
        //     if (all-A[ind]-A[i] <= b) {
        //         System.out.println("YES");
        //         System.exit(0);
        //     }
        // }

        // System.out.println("NO");
        
    }    
}