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.util.*;

import java.util.Scanner;

public class Main {
    public static void main(String[] args){
        int n = scanner.nextInt();
        int[] a = new int[n];
        int[] b = new int[n];
        readArray(a);readArray(b);
        long sum = Arraysum(a);
        Arrays.sort(b);
        long sum2 = b[b.length-1]+b[b.length-2];
        if(sum2<sum){
            System.out.println("NO");
        }else {
            System.out.println("YES");
        }
    }
    private static String revString(String str){
        StringBuilder sb = new StringBuilder(str);
        sb.reverse();
        return sb.toString();
    }
    private static int fibo(int n){
        if(n==0){
            return 0;
        }
        if(n==1){
            return 1;
        }
        return fibo(n-1)+fibo(n-2);
    }
    private static void swap(char[] array , int a,int b){
        if(a==b){
            return;
        }
        char temp = array[a];
        array[a] = array[b];
        array[b] = temp;
    }
    private static Scanner scanner = new Scanner(System.in);
    private static int max(int[] array ){
        int min = Integer.MIN_VALUE;
        for(int i = 0;i< array.length;i++){
            if(array[i]>min){
                min = array[i];
            }
        }
        return min;
    }
    private static int min(int[] array ){
        int min = Integer.MAX_VALUE;
        for(int i = 0;i< array.length;i++){
            if(array[i]<min){
                min = array[i];
            }
        }
        return min;
    }
    private static void readArray(int[] array){
        for(int i = 0;i< array.length;i++){
            array[i] = scanner.nextInt();
        }
    }
    private static void printarray(int[] array){
        for(int i = 0; i< array.length;i++){
            System.out.print(array[i]);
        }
    }
    private static int gcd(int a , int b){
        if(b==0) return  a;
        else return gcd(b,a%b);
    }
    private static long fact(int n){
        if(n==1 || n==0) return 1;
        else return (long) n*fact(n-1);
    }
    private static long Arraysum(int[] array){
        long sum = 0;
        for(int i = 0 ;i< array.length;i++){
            sum+=array[i];
        }
        return sum;
    }
    private static boolean isPrime(long n){
        if(n==1){
            return false;
        }
        for(long i = 2;i<=Math.sqrt(n);i++){
            if(n%i==0){
                return false;
            }
        }
        return true;
    }
    private static int multiply(int[] array){
        int mult = 1 ;
        for(int i = 0 ;i< array.length;i++) {
            mult *= array[i];
        }
        return mult;
    }
    private static int FromStringtoInt(String s){
        s = s.replaceAll("[^0-9]","");
        return Integer.parseInt(s);
    }

}