Note that the memory limit is unusual.

You are given an integer n and two sequences a_1, a_2, ..., a_n and b_1, b_2, ..., b_n.

Let's call a set of integers S such that S ⊆ \{1, 2, 3, ..., n\} strange, if, for every element i of S, the following condition is met: for every j ∈ [1, i - 1], if a_j divides a_i, then j is also included in S. An empty set is always strange.

The cost of the set S is ∑_{i ∈ S} b_i. You have to calculate the maximum possible cost of a strange set.

Input

The first line contains one integer n (1 ≤ n ≤ 3000).

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 100).

The third line contains n integers b_1, b_2, ..., b_n (-10^5 ≤ b_i ≤ 10^5).

Output

Print one integer — the maximum cost of a strange set.

Examples

Input


9
4 7 3 4 5 6 7 8 13
-2 3 -19 5 -6 7 -8 9 1


Output


16


Input


2
42 42
-37 13


Output


0


Input


2
42 42
13 -37


Output


13

Note

The strange set with the maximum cost in the first example is \{1, 2, 4, 8, 9\}.

The strange set with the maximum cost in the second example is empty.
from typing import NamedTuple, Optional, List, cast


class MFGraph:
    class Edge(NamedTuple):
        src: int
        dst: int
        cap: int
        flow: int

    class _Edge:
        def __init__(self, dst: int, cap: int) -> None:
            self.dst = dst
            self.cap = cap
            self.rev: Optional[MFGraph._Edge] = None

    def __init__(self, n: int) -> None:
        self._n = n
        self._g: List[List[MFGraph._Edge]] = [[] for _ in range(n)]
        self._edges: List[MFGraph._Edge] = []

    def add_edge(self, src: int, dst: int, cap: int) -> int:
        assert 0 <= src < self._n
        assert 0 <= dst < self._n
        assert 0 <= cap
        m = len(self._edges)
        e = MFGraph._Edge(dst, cap)
        re = MFGraph._Edge(src, 0)
        e.rev = re
        re.rev = e
        self._g[src].append(e)
        self._g[dst].append(re)
        self._edges.append(e)
        return m

    def get_edge(self, i: int) -> Edge:
        assert 0 <= i < len(self._edges)
        e = self._edges[i]
        re = cast(MFGraph._Edge, e.rev)
        return MFGraph.Edge(
            re.dst,
            e.dst,
            e.cap + re.cap,
            re.cap
        )

    def edges(self) -> List[Edge]:
        return [self.get_edge(i) for i in range(len(self._edges))]

    def change_edge(self, i: int, new_cap: int, new_flow: int) -> None:
        assert 0 <= i < len(self._edges)
        assert 0 <= new_flow <= new_cap
        e = self._edges[i]
        e.cap = new_cap - new_flow
        assert e.rev is not None
        e.rev.cap = new_flow

    def flow(self, s: int, t: int, flow_limit: Optional[int] = None) -> int:
        assert 0 <= s < self._n
        assert 0 <= t < self._n
        assert s != t
        if flow_limit is None:
            flow_limit = cast(int, sum(e.cap for e in self._g[s]))

        current_edge = [0] * self._n
        level = [0] * self._n

        def fill(arr: List[int], value: int) -> None:
            for i in range(len(arr)):
                arr[i] = value

        def bfs() -> bool:
            fill(level, self._n)
            queue = []
            q_front = 0
            queue.append(s)
            level[s] = 0
            while q_front < len(queue):
                v = queue[q_front]
                q_front += 1
                next_level = level[v] + 1
                for e in self._g[v]:
                    if e.cap == 0 or level[e.dst] <= next_level:
                        continue
                    level[e.dst] = next_level
                    if e.dst == t:
                        return True
                    queue.append(e.dst)
            return False

        def dfs(lim: int) -> int:
            stack = []
            edge_stack: List[MFGraph._Edge] = []
            stack.append(t)
            while stack:
                v = stack[-1]
                if v == s:
                    flow = min(lim, min(e.cap for e in edge_stack))
                    for e in edge_stack:
                        e.cap -= flow
                        assert e.rev is not None
                        e.rev.cap += flow
                    return flow
                next_level = level[v] - 1
                while current_edge[v] < len(self._g[v]):
                    e = self._g[v][current_edge[v]]
                    re = cast(MFGraph._Edge, e.rev)
                    if level[e.dst] != next_level or re.cap == 0:
                        current_edge[v] += 1
                        continue
                    stack.append(e.dst)
                    edge_stack.append(re)
                    break
                else:
                    stack.pop()
                    if edge_stack:
                        edge_stack.pop()
                    level[v] = self._n
            return 0

        flow = 0
        while flow < flow_limit:
            if not bfs():
                break
            fill(current_edge, 0)
            while flow < flow_limit:
                f = dfs(flow_limit - flow)
                flow += f
                if f == 0:
                    break
        return flow

    def min_cut(self, s: int) -> List[bool]:
        visited = [False] * self._n
        stack = [s]
        visited[s] = True
        while stack:
            v = stack.pop()
            for e in self._g[v]:
                if e.cap > 0 and not visited[e.dst]:
                    visited[e.dst] = True
                    stack.append(e.dst)
        return visited
INF=10**20
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
k=max(b)
if k<=0:
  print(0)
  exit()
g=MFGraph(n+2)
for i in range(n):
  b[i]=k-b[i]
for i in range(n):
  g.add_edge(n,i,b[i])
  g.add_edge(i,n+1,k)
for i in range(n):
  q=[0]*101
  for j in range(i-1,-1,-1):
    if a[i]%a[j]==0 and q[a[j]]==0:
      q[a[j]]=1
      g.add_edge(j,i,INF)
print(k*n-g.flow(n,n+1))
