Problem: Let's denote the following function f. This function takes an array a of length n and returns an array. Initially the result is an empty array. For each integer i from 1 to n we add element a_i to the end of the resulting array if it is greater than all previous elements (more formally, if a_i > max_{1 ≤ j < i}a_j). Some examples of the function f:

  1. if a = [3, 1, 2, 7, 7, 3, 6, 7, 8] then f(a) = [3, 7, 8]; 
  2. if a = [1] then f(a) = [1]; 
  3. if a = [4, 1, 1, 2, 3] then f(a) = [4]; 
  4. if a = [1, 3, 1, 2, 6, 8, 7, 7, 4, 11, 10] then f(a) = [1, 3, 6, 8, 11]. 



You are given two arrays: array a_1, a_2, ... , a_n and array b_1, b_2, ... , b_m. You can delete some elements of array a (possibly zero). To delete the element a_i, you have to pay p_i coins (the value of p_i can be negative, then you get |p_i| coins, if you delete this element). Calculate the minimum number of coins (possibly negative) you have to spend for fulfilling equality f(a) = b.

Input

The first line contains one integer n (1 ≤ n ≤ 5 ⋅ 10^5) — the length of array a.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n) — the array a.

The third line contains n integers p_1, p_2, ..., p_n (|p_i| ≤ 10^9) — the array p.

The fourth line contains one integer m (1 ≤ m ≤ n) — the length of array b.

The fifth line contains m integers b_1, b_2, ..., b_m (1 ≤ b_i ≤ n, b_{i-1} < b_i) — the array b.

Output

If the answer exists, in the first line print YES. In the second line, print the minimum number of coins you have to spend for fulfilling equality f(a) = b.

Otherwise in only line print NO.

Examples

Input


11
4 1 3 3 7 8 7 9 10 7 11
3 5 0 -2 5 3 6 7 8 2 4
3
3 7 10


Output


YES
20


Input


6
2 1 5 3 6 5
3 -9 0 16 22 -14
4
2 3 5 6


Output


NO

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long mod = 1e9 + 7;
template <class T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class S, class T>
ostream &operator<<(ostream &os, const pair<S, T> v) {
  os << "(" << v.first << ", " << v.second << ")";
  return os;
}
template <class T>
ostream &operator<<(ostream &os, const vector<T> v) {
  for (int i = 0; i < (int)v.size(); i++) {
    if (i > 0) {
      os << " ";
    }
    os << v[i];
  }
  return os;
}
template <class T>
ostream &operator<<(ostream &os, const vector<vector<T>> v) {
  for (int i = 0; i < (int)v.size(); i++) {
    if (i > 0) {
      os << endl;
    }
    os << v[i];
  }
  return os;
}
string num2bit(long long num, long long len) {
  string bit = "";
  for (int i = 0; i < (int)len; ++i) {
    bit += char('0' + (num >> i & 1));
  }
  return bit;
}
template <typename Monoid, typename OperatorMonoid, typename F, typename G,
          typename H>
struct LazySegmentTree {
  int sz, height;
  vector<Monoid> data;
  vector<OperatorMonoid> lazy;
  const F f;
  const G g;
  const H h;
  const Monoid M1;
  const OperatorMonoid OM0;
  LazySegmentTree(int n, const F f, const G g, const H h, const Monoid &M1,
                  const OperatorMonoid OM0)
      : f(f), g(g), h(h), M1(M1), OM0(OM0) {
    sz = 1;
    height = 0;
    while (sz < n) sz <<= 1, height++;
    data.assign(2 * sz, M1);
    lazy.assign(2 * sz, OM0);
  }
  void set(int k, const Monoid &x) { data[k + sz] = x; }
  void build() {
    for (int k = sz - 1; k > 0; k--) {
      data[k] = f(data[2 * k + 0], data[2 * k + 1]);
    }
  }
  inline void propagate(int k) {
    if (lazy[k] != OM0) {
      lazy[2 * k + 0] = h(lazy[2 * k + 0], lazy[k]);
      lazy[2 * k + 1] = h(lazy[2 * k + 1], lazy[k]);
      data[k] = reflect(k);
      lazy[k] = OM0;
    }
  }
  inline Monoid reflect(int k) {
    return lazy[k] == OM0 ? data[k] : g(data[k], lazy[k]);
  }
  inline void recalc(int k) {
    while (k >>= 1) data[k] = f(reflect(2 * k + 0), reflect(2 * k + 1));
  }
  inline void thrust(int k) {
    for (int i = height; i > 0; i--) propagate(k >> i);
  }
  void update(int a, int b, const OperatorMonoid &x) {
    thrust(a += sz);
    thrust(b += sz - 1);
    for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
      if (l & 1) lazy[l] = h(lazy[l], x), ++l;
      if (r & 1) --r, lazy[r] = h(lazy[r], x);
    }
    recalc(a);
    recalc(b);
  }
  Monoid query(int a, int b) {
    thrust(a += sz);
    thrust(b += sz - 1);
    Monoid L = M1, R = M1;
    for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
      if (l & 1) L = f(L, reflect(l++));
      if (r & 1) R = f(reflect(--r), R);
    }
    return f(L, R);
  }
  Monoid operator[](const int &k) { return query(k, k + 1); }
  template <typename C>
  int find_subtree(int a, const C &check, Monoid &M, bool type) {
    while (a < sz) {
      propagate(a);
      Monoid nxt =
          type ? f(reflect(2 * a + type), M) : f(M, reflect(2 * a + type));
      if (check(nxt))
        a = 2 * a + type;
      else
        M = nxt, a = 2 * a + 1 - type;
    }
    return a - sz;
  }
  template <typename C>
  int find_first(int a, const C &check) {
    Monoid L = M1;
    if (a <= 0) {
      if (check(f(L, reflect(1)))) return find_subtree(1, check, L, false);
      return -1;
    }
    thrust(a + sz);
    int b = sz;
    for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if (a & 1) {
        Monoid nxt = f(L, reflect(a));
        if (check(nxt)) return find_subtree(a, check, L, false);
        L = nxt;
        ++a;
      }
    }
    return -1;
  }
  template <typename C>
  int find_last(int b, const C &check) {
    Monoid R = M1;
    if (b >= sz) {
      if (check(f(reflect(1), R))) return find_subtree(1, check, R, true);
      return -1;
    }
    thrust(b + sz - 1);
    int a = sz;
    for (b += sz; a < b; a >>= 1, b >>= 1) {
      if (b & 1) {
        Monoid nxt = f(reflect(--b), R);
        if (check(nxt)) return find_subtree(b, check, R, true);
        R = nxt;
      }
    }
    return -1;
  }
};
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  const long long INF = (1ll << 60);
  long long n;
  cin >> n;
  vector<long long> a(n), p(n);
  for (int i = 0; i < (int)n; ++i) cin >> a[i];
  for (int i = 0; i < (int)n; ++i) cin >> p[i];
  long long m;
  cin >> m;
  vector<long long> b(m + 1);
  b[0] = -INF;
  for (int i = 0; i < (int)m; ++i) cin >> b[i + 1];
  auto f = [](long long x, long long y) { return min(x, y); };
  auto g = [](long long x, long long a) { return x + a; };
  auto h = [](long long a, long long b) { return a + b; };
  long long M1 = INF;
  long long OM0 = 0;
  LazySegmentTree<long long, long long, decltype(f), decltype(g), decltype(h)>
      seg(m + 1, f, g, h, M1, OM0);
  for (int i = 0; i < (int)m + 1; ++i) seg.set(i, INF);
  seg.set(0, 0);
  seg.build();
  long long pos2 = 1;
  for (int i = 0; i < (int)n; ++i) {
    long long pos1 = lower_bound(b.begin(), b.end(), a[i]) - b.begin();
    long long pos = min(pos1, pos2);
    long long prev = seg[pos1 - 1];
    if (p[i] > 0) {
      seg.update(0, pos, p[i]);
    } else {
      seg.update(0, pos2, p[i]);
    }
    if (pos1 <= m and b[pos1] == a[i]) {
      long long val = min(seg[pos1], prev);
      long long tasu = val - seg[pos1];
      seg.update(pos1, pos1 + 1, tasu);
      if (pos1 == pos2) pos2++;
    }
  }
  cout << (seg[m] == INF ? "NO\n" : "YES\n");
  if (seg[m] != INF) cout << seg[m] << endl;
  return 0;
}