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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
inline long long input() {
  int32_t x;
  scanf("%d", &x);
  return x;
}
inline long long in() {
  int32_t x;
  scanf("%d", &x);
  return x;
}
const long long maxn = 2e5 + 10;
const long long mod = 1e9 + 7;
long long a[maxn], b[maxn];
int32_t main() {
  long long n = in();
  long long sum = 0;
  for (long long i = 0; i < n; i++) a[i] = in(), sum += a[i];
  for (long long i = 0; i < n; i++) b[i] = in();
  sort(b, b + n, greater<long long>());
  long long ss = b[0] + b[1];
  if (ss >= sum)
    return cout << "YES\n", 0;
  else
    cout << "NO\n";
}