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.*;
public class W11P1 {
//	public static void main(String[] args) {
//		Scanner sc = new Scanner(System.in);
//		double K = (double)sc.nextInt();
//		double P = (double)sc.nextInt();
//		double X = (double)sc.nextInt();
//		sc.close();
//		double result = Math.sqrt(K * P / X);
//		double t1 = Math.round(result);
//		double t2 = t1+1;
//		double t3 = t1-1;
//		
//		double r1 = K * P / t1 + X * t1;
//		double r2 = K * P / t2 + X * t2;
//		double r3 = K * P / t3 + X * t3;
//		
//		System.out.println(String.format("%.3f", Math.min(r1, Math.min(r2, r3))));
//	}
//	public static void main(String[] args) {
//		Scanner sc = new Scanner(System.in);
//		int n = sc.nextInt();
//		int X = sc.nextInt();
//		double v = sc.nextDouble();
//		double num = 0;
//		for (int i = 0; i < n; i++) {
//			int l = sc.nextInt();
//			int r = sc.nextInt();
//			double vi = sc.nextDouble();
//			num -= (r - l) * vi;
//		}
//		sc.close();
//		double sin = num / (X * v);
//		if (sin * sin > 0.75)
//			System.out.println("Too hard");
//		else {
//			double speed = v * Math.sqrt(1 - sin*sin);
//			System.out.println(String.format("%.3f",X/speed));
//		}
//	}
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int num = sc.nextInt();
		long total = 0;
		for (int i = 0; i < num; i++) {
			total += sc.nextInt();
		}
		long[] cap = new long[num];
		for (int i = 0; i < num; i++) {
			cap[i] = sc.nextLong();
		}
		Arrays.sort(cap);
		if (cap[cap.length-1] + cap[cap.length-2] < total) {
			System.out.println("NO");
		} else {
			System.out.println("YES");
		}
	}
}