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;
using ll = long long;
const int MOD = 1000000007;
const int MOD2 = 998244353;
const int INF = 1 << 30;
const ll INF2 = (ll)1 << 60;
void scan(int& a) { scanf("%d", &a); }
void scan(long long& a) { scanf("%lld", &a); }
template <class T, class L>
void scan(pair<T, L>& p) {
  scan(p.first);
  scan(p.second);
}
template <class T, class U, class V>
void scan(tuple<T, U, V>& p) {
  scan(get<0>(p));
  scan(get<1>(p));
  scan(get<2>(p));
}
template <class T>
void scan(T& a) {
  cin >> a;
}
template <class T>
void scan(vector<T>& vec) {
  for (auto&& it : vec) scan(it);
}
void in() {}
template <class Head, class... Tail>
void in(Head& head, Tail&... tail) {
  scan(head);
  in(tail...);
}
void print(const int& a) { printf("%d", a); }
void print(const long long& a) { printf("%lld", a); }
void print(const double& a) { printf("%.15lf", a); }
template <class T, class L>
void print(const pair<T, L>& p) {
  print(p.first);
  putchar(' ');
  print(p.second);
}
template <class T>
void print(const T& a) {
  cout << a;
}
template <class T>
void print(const vector<T>& vec) {
  if (vec.empty()) return;
  print(vec[0]);
  for (auto it = vec.begin(); ++it != vec.end();) {
    putchar(' ');
    print(*it);
  }
}
void out() { putchar('\n'); }
template <class T>
void out(const T& t) {
  print(t);
  putchar('\n');
}
template <class Head, class... Tail>
void out(const Head& head, const Tail&... tail) {
  print(head);
  putchar(' ');
  out(tail...);
}
template <class T>
void dprint(const T& a) {
  cerr << a;
}
template <class T>
void dprint(const vector<T>& vec) {
  if (vec.empty()) return;
  cerr << vec[0];
  for (auto it = vec.begin(); ++it != vec.end();) {
    cerr << " " << *it;
  }
}
void debug() { cerr << endl; }
template <class T>
void debug(const T& t) {
  dprint(t);
  cerr << endl;
}
template <class Head, class... Tail>
void debug(const Head& head, const Tail&... tail) {
  dprint(head);
  cerr << " ";
  debug(tail...);
}
ll intpow(ll a, ll b) {
  ll ans = 1;
  while (b) {
    if (b & 1) ans *= a;
    a *= a;
    b /= 2;
  }
  return ans;
}
ll modpow(ll a, ll b, ll p) {
  ll ans = 1;
  while (b) {
    if (b & 1) (ans *= a) %= p;
    (a *= a) %= p;
    b /= 2;
  }
  return ans;
}
ll modinv(ll a, ll m) {
  ll b = m, u = 1, v = 0;
  while (b) {
    ll t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= m;
  if (u < 0) u += m;
  return u;
}
ll updivide(ll a, ll b) {
  if (a % b == 0)
    return a / b;
  else
    return (a / b) + 1;
}
template <class T>
void chmax(T& a, const T b) {
  if (b > a) a = b;
}
template <class T>
void chmin(T& a, const T b) {
  if (b < a) a = b;
}
int main() {
  int n;
  in(n);
  vector<ll> a(n), b(n);
  in(a, b);
  ll sumv = 0;
  for (int i = 0; i < (int)(n); i++) sumv += a[i];
  sort(b.rbegin(), b.rend());
  if (sumv <= b[0] + b[1])
    printf("YES\n");
  else
    printf("NO\n");
}