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>
typedef struct {
  int len;
  unsigned long long cap[100000];
  unsigned long long vol[100000];
} cans;
void read_elements(cans* a) {
  int i;
  for (i = 0; i < a->len; i++) {
    scanf("%llu", &a->vol[i]);
  }
  for (i = 0; i < a->len; i++) {
    scanf("%llu", &a->cap[i]);
  }
}
unsigned long long array_max2add(int len, unsigned long long* dat) {
  unsigned long long max1 = 0;
  unsigned long long max2 = 0;
  int i;
  for (i = 0; i < len; i++) {
    unsigned long long c = dat[i];
    if (c >= max1) {
      max2 = max1;
      max1 = c;
    } else if (c > max2) {
      max2 = c;
    }
  }
  return max1 + max2;
}
unsigned long long array_sum(int len, unsigned long long arr[]) {
  unsigned long long sum = 0;
  int i;
  for (i = 0; i < len; i++) {
    sum += arr[i];
  }
  return sum;
}
int simulate(cans* a) {
  unsigned long long cap = array_max2add(a->len, a->cap);
  unsigned long long sum = array_sum(a->len, a->vol);
  return cap >= sum;
}
int main(int argc, char* argv[]) {
  cans c = {};
  scanf("%i", &c.len);
  read_elements(&c);
  int exit_state = simulate(&c);
  printf("%s\n", exit_state ? "YES" : "NO");
  return EXIT_SUCCESS;
}