There are many blue cards and red cards on the table. For each card, an integer number greater than 1 is printed on its face. The same number may be printed on several cards.

A blue card and a red card can be paired when both of the numbers printed on them have a common divisor greater than 1. There may be more than one red card that can be paired with one blue card. Also, there may be more than one blue card that can be paired with one red card. When a blue card and a red card are chosen and paired, these two cards are removed from the whole cards on the table.

<image>
Figure E-1: Four blue cards and three red cards

For example, in Figure E-1, there are four blue cards and three red cards. Numbers 2, 6, 6 and 15 are printed on the faces of the four blue cards, and 2, 3 and 35 are printed on those of the three red cards. Here, you can make pairs of blue cards and red cards as follows. First, the blue card with number 2 on it and the red card with 2 are paired and removed. Second, one of the two blue cards with 6 and the red card with 3 are paired and removed. Finally, the blue card with 15 and the red card with 35 are paired and removed. Thus the number of removed pairs is three.

Note that the total number of the pairs depends on the way of choosing cards to be paired. The blue card with 15 and the red card with 3 might be paired and removed at the beginning. In this case, there are only one more pair that can be removed and the total number of the removed pairs is two.

Your job is to find the largest number of pairs that can be removed from the given set of cards on the table.

Input

The input is a sequence of datasets. The number of the datasets is less than or equal to 100. Each dataset is formatted as follows.

> m n
>  b1 ... bk ... bm
>  r1 ... rk ... rn
>

The integers m and n are the number of blue cards and that of red cards, respectively. You may assume 1 ≤ m ≤ 500 and 1≤ n ≤ 500. bk (1 ≤ k ≤ m) and rk (1 ≤ k ≤ n) are numbers printed on the blue cards and the red cards respectively, that are integers greater than or equal to 2 and less than 10000000 (=107). The input integers are separated by a space or a newline. Each of bm and rn is followed by a newline. There are no other characters in the dataset.

The end of the input is indicated by a line containing two zeros separated by a space.

Output

For each dataset, output a line containing an integer that indicates the maximum of the number of the pairs.

Sample Input


4 3
2 6 6 15
2 3 5
2 3
4 9
8 16 32
4 2
4 9 11 13
5 7
5 5
2 3 5 1001 1001
7 11 13 30 30
10 10
2 3 5 7 9 11 13 15 17 29
4 6 10 14 18 22 26 30 34 38
20 20
195 144 903 63 137 513 44 626 75 473
876 421 568 519 755 840 374 368 570 872
363 650 155 265 64 26 426 391 15 421
373 984 564 54 823 477 565 866 879 638
100 100
195 144 903 63 137 513 44 626 75 473
876 421 568 519 755 840 374 368 570 872
363 650 155 265 64 26 426 391 15 421
373 984 564 54 823 477 565 866 879 638
117 755 835 683 52 369 302 424 513 870
75 874 299 228 140 361 30 342 750 819
761 123 804 325 952 405 578 517 49 457
932 941 988 767 624 41 912 702 241 426
351 92 300 648 318 216 785 347 556 535
166 318 434 746 419 386 928 996 680 975
231 390 916 220 933 319 37 846 797 54
272 924 145 348 350 239 563 135 362 119
446 305 213 879 51 631 43 755 405 499
509 412 887 203 408 821 298 443 445 96
274 715 796 417 839 147 654 402 280 17
298 725 98 287 382 923 694 201 679 99
699 188 288 364 389 694 185 464 138 406
558 188 897 354 603 737 277 35 139 556
826 213 59 922 499 217 846 193 416 525
69 115 489 355 256 654 49 439 118 961
0 0


Output for the Sample Input


3
1
0
4
9
18
85






Example

Input

4 3
2 6 6 15
2 3 5
2 3
4 9
8 16 32
4 2
4 9 11 13
5 7
5 5
2 3 5 1001 1001
7 11 13 30 30
10 10
2 3 5 7 9 11 13 15 17 29
4 6 10 14 18 22 26 30 34 38
20 20
195 144 903 63 137 513 44 626 75 473
876 421 568 519 755 840 374 368 570 872
363 650 155 265 64 26 426 391 15 421
373 984 564 54 823 477 565 866 879 638
100 100
195 144 903 63 137 513 44 626 75 473
876 421 568 519 755 840 374 368 570 872
363 650 155 265 64 26 426 391 15 421
373 984 564 54 823 477 565 866 879 638
117 755 835 683 52 369 302 424 513 870
75 874 299 228 140 361 30 342 750 819
761 123 804 325 952 405 578 517 49 457
932 941 988 767 624 41 912 702 241 426
351 92 300 648 318 216 785 347 556 535
166 318 434 746 419 386 928 996 680 975
231 390 916 220 933 319 37 846 797 54
272 924 145 348 350 239 563 135 362 119
446 305 213 879 51 631 43 755 405 499
509 412 887 203 408 821 298 443 445 96
274 715 796 417 839 147 654 402 280 17
298 725 98 287 382 923 694 201 679 99
699 188 288 364 389 694 185 464 138 406
558 188 897 354 603 737 277 35 139 556
826 213 59 922 499 217 846 193 416 525
69 115 489 355 256 654 49 439 118 961
0 0


Output

3
1
0
4
9
18
85

Difficulty: UNKNOWN_DIFFICULTY

Solutions:
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians, gcd
from itertools import accumulate, permutations, combinations, product, groupby, combinations_with_replacement
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left
from heapq import heappush, heappop
from functools import reduce

def input():
	return sys.stdin.readline().strip()

def INT():
	return int(input())

def MAP():
	return map(int, input().split())

def LIST():
	return list(map(int, input().split()))

def ZIP(n):
	return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

class Dinic:

	def __init__(self, n):
		self.n = n
		self.g = [[] for i in range(n)]

	def add_edge(self, fr, to, cap):
		forward = [to, cap, None]
		forward[2] = backward = [fr, 0, forward]
		self.g[fr].append(forward)
		self.g[to].append(backward)

	def add_bidirectional_edge(self, v1, v2, cap1, cap2):
		edge1 = [v2, cap1, None]
		edge1[2] = edge2 = [v1, cap2, edge1]
		self.g[v1].append(edge1)
		self.g[v2].append(edge2)

	def bfs(self, s, t):
		self.level = level = [None] * self.n
		deq = deque([s])
		level[s] = 0
		g = self.g
		while deq:
			v = deq.popleft()
			lv = level[v] + 1
			for (w, cap, _) in g[v]:
				if cap and level[w] is None:
					level[w] = lv
					deq.append(w)
		return level[t] is not None

	def dfs(self, v, t, f):
		if v == t:
			return f
		level = self.level
		for e in self.it[v]:
			(w, cap, rev) = e
			if cap and level[v] < level[w]:
				d = self.dfs(w, t, min(f, cap))
				if d:
					e[1] -= d
					rev[1] += d
					return d
		return 0

	def flow(self, s, t):
		flow = 0
		INF = 10 ** 30
		g = self.g
		while self.bfs(s, t):
			self.it = list(map(iter, self.g))
			f = INF
			while f:
				f = self.dfs(s, t, INF)
				flow += f
		return flow
ans = []
while 1:
	(m, n) = MAP()
	if m == 0:
		break
	D = Dinic(m + n + 2)
	B = LIST()
	while len(B) < m:
		B += LIST()
	R = LIST()
	while len(R) < n:
		R += LIST()
	s = m + n
	t = s + 1
	for i in range(m):
		D.add_edge(s, i, 1)
	for i in range(n):
		D.add_edge(m + i, t, 1)
	for (i, x) in enumerate(B):
		for (j, y) in enumerate(R):
			if gcd(x, y) != 1:
				D.add_edge(i, m + j, 1)
	ans.append(D.flow(s, t))
print(*ans, sep='\n')


import math
from collections import deque

class MaxFlow:

	class Edge:

		def __init__(self, to, cap, rev):
			self.to = to
			self.cap = cap
			self.rev = rev

	def __init__(self, n, inf=10 ** 9 + 7):
		self.n = n
		self.inf = inf
		self.level = [-1] * n
		self.iter = [0] * n
		self.e = [[] for _ in range(n)]

	def add_edge(self, from_, to, cap):
		self.e[from_].append(self.Edge(to, cap, len(self.e[to])))
		self.e[to].append(self.Edge(from_, 0, len(self.e[from_]) - 1))

	def bfs(self, start):
		self.level = [-1] * self.n
		dq = deque()
		self.level[start] = 0
		dq.append(start)
		while dq:
			cur_vertex = dq.popleft()
			for edge in self.e[cur_vertex]:
				if edge.cap > 0 > self.level[edge.to]:
					self.level[edge.to] = self.level[cur_vertex] + 1
					dq.append(edge.to)

	def dfs(self, cur_vertex, end_vertex, flow):
		if cur_vertex == end_vertex:
			return flow
		while self.iter[cur_vertex] < len(self.e[cur_vertex]):
			edge = self.e[cur_vertex][self.iter[cur_vertex]]
			if edge.cap > 0 and self.level[cur_vertex] < self.level[edge.to]:
				flowed = self.dfs(edge.to, end_vertex, min(flow, edge.cap))
				if flowed > 0:
					edge.cap -= flowed
					self.e[edge.to][edge.rev].cap += flowed
					return flowed
			self.iter[cur_vertex] += 1
		return 0

	def compute(self, source, sink):
		flow = 0
		while True:
			self.bfs(source)
			if self.level[sink] < 0:
				return flow
			self.iter = [0] * self.n
			while True:
				f = self.dfs(source, sink, self.inf)
				if f == 0:
					break
				flow += f

def main():
	while True:
		(n, m) = map(int, input().split())
		if n == 0:
			break
		a = []
		while True:
			c = list(map(int, input().split()))
			a.extend(c)
			if len(a) >= n:
				break
		b = []
		while True:
			c = list(map(int, input().split()))
			b.extend(c)
			if len(b) >= m:
				break
		MF = MaxFlow(n + m + 2)
		s = n + m
		t = n + m + 1
		for i in range(n):
			for j in range(m):
				if math.gcd(a[i], b[j]) != 1:
					MF.add_edge(i, j + n, 1)
		for i in range(n):
			MF.add_edge(s, i, 1)
		for i in range(m):
			MF.add_edge(i + n, t, 1)
		print(MF.compute(s, t))
main()


import sys, queue, math, copy, itertools, bisect, collections, heapq

def main():
	LI = lambda : [int(x) for x in sys.stdin.readline().split()]
	while True:
		(m, n) = LI()
		if m + n == 0:
			return
		goal = m + n + 1
		b = []
		r = []
		for _ in range((m - 1) // 10 + 1):
			b.extend(LI())
		for _ in range((n - 1) // 10 + 1):
			r.extend(LI())
		edge = [set() for _ in range(goal + 1)]
		for i in range(1, m + 1):
			edge[0].add(i)
		for i in range(m + 1, goal + 1):
			edge[i].add(goal)
		for i in range(m):
			for j in range(n):
				if math.gcd(b[i], r[j]) > 1:
					edge[i + 1].add(j + m + 1)
		ans = 0
		while True:
			node = [-1] * (goal + 1)
			q = collections.deque()
			node[0] = 0
			q.append(0)
			while q:
				u = q.pop()
				for v in edge[u]:
					if node[v] >= 0:
						continue
					node[v] = u
					if v == goal:
						ans += 1
						break
					q.append(v)
				else:
					continue
				break
			else:
				break
			v = goal
			while v > 0:
				u = node[v]
				edge[u].remove(v)
				edge[v].add(u)
				v = u
		print(ans)
main()


from collections import deque

class Dinic(object):
	__slots__ = ['inf', 'v_count', 'edges', 'iter', 'level']

	def __init__(self, v_count: int, edges: list):
		self.inf = 10 ** 9
		self.v_count = v_count
		self.edges = [[] for _ in [0] * v_count]
		self.iter = [0] * v_count
		self.level = None
		self._create_graph(edges)

	def _create_graph(self, _edges):
		edges = self.edges
		for (origin, dest, cap) in _edges:
			edges[origin].append([dest, cap, len(edges[dest])])
			edges[dest].append([origin, 0, len(edges[origin]) - 1])

	def solve(self, source: int, sink: int):
		max_flow = 0
		while True:
			self.bfs(source)
			if self.level[sink] < 0:
				return max_flow
			self.iter = [0] * self.v_count
			flow = self.dfs(source, sink, self.inf)
			while flow > 0:
				max_flow += flow
				flow = self.dfs(source, sink, self.inf)

	def bfs(self, source: int):
		(level, edges) = ([-1] * self.v_count, self.edges)
		level[source] = 0
		dq = deque([source])
		(popleft, append) = (dq.popleft, dq.append)
		while dq:
			v = popleft()
			for (dest, cap, _rev) in edges[v]:
				if cap > 0 > level[dest]:
					level[dest] = level[v] + 1
					append(dest)
		self.level = level

	def dfs(self, source: int, sink: int, flow: int) -> int:
		if source == sink:
			return flow
		while self.iter[source] < len(self.edges[source]):
			(dest, cap, rev) = edge = self.edges[source][self.iter[source]]
			if cap > 0 and self.level[source] < self.level[dest]:
				flowed = self.dfs(dest, sink, flow if flow < cap else cap)
				if flowed > 0:
					edge[1] -= flowed
					self.edges[dest][rev][1] += flowed
					return flowed
			self.iter[source] += 1
		return 0

def get_prime_set(ub):
	from itertools import chain
	from math import sqrt
	if ub < 4:
		return ({}, {}, {2}, {2, 3})[ub]
	(ub, ub_sqrt) = (ub + 1, int(sqrt(ub)) + 1)
	primes = {2, 3} | set(chain(range(5, ub, 6), range(7, ub, 6)))
	du = primes.difference_update
	for n in chain(range(5, ub_sqrt, 6), range(7, ub_sqrt, 6)):
		if n in primes:
			du(range(n * 3, ub, n * 2))
	return primes
from math import sqrt
from collections import defaultdict
primes = get_prime_set(int(sqrt(10 ** 7)) + 1)
answer = []
append_answer = answer.append
while True:
	(M, N) = map(int, input().split())
	if not M * N:
		break
	(source, sink) = (M + N, M + N + 1)
	(edges, blue, red) = ([], [], [])
	for i in range(M):
		edges.append((i, sink, 1))
	for i in range(M, M + N):
		edges.append((source, i, 1))
	divisors = defaultdict(set)
	index = 0
	while index < M:
		for num in map(int, input().split()):
			for p in filter(lambda x: num % x == 0, primes):
				divisors[p].add(index)
				while num % p == 0:
					num //= p
			if num > 1:
				divisors[num].add(index)
			index += 1
	while index < M + N:
		for num in map(int, input().split()):
			neighbors = set()
			update = neighbors.update
			for p in filter(lambda x: num % x == 0, primes):
				update(divisors[p])
				while num % p == 0:
					num //= p
			if num > 1:
				update(divisors[num])
			for dest in neighbors:
				edges.append((index, dest, 1))
			index += 1
	dinic = Dinic(sink + 1, edges)
	append_answer(dinic.solve(source, sink))
print(*answer, sep='\n')


import sys
readline = sys.stdin.buffer.readline

def even(n):
	return 1 if n % 2 == 0 else 0
import queue

class Dinic:

	def __init__(self, v, inf=10 ** 10):
		self.V = v
		self.inf = inf
		self.G = [[] for _ in range(v)]
		self.level = [0 for _ in range(v)]
		self.iter = [0 for _ in range(v)]

	def add_edge(self, from_, to, cap):
		self.G[from_].append({'to': to, 'cap': cap, 'rev': len(self.G[to])})
		self.G[to].append({'to': from_, 'cap': 0, 'rev': len(self.G[from_]) - 1})

	def bfs(self, s):
		self.level = [-1 for _ in range(self.V)]
		self.level[s] = 0
		que = queue.Queue()
		que.put(s)
		while not que.empty():
			v = que.get()
			for i in range(len(self.G[v])):
				e = self.G[v][i]
				if e['cap'] > 0 and self.level[e['to']] < 0:
					self.level[e['to']] = self.level[v] + 1
					que.put(e['to'])

	def dfs(self, v, t, f):
		if v == t:
			return f
		for i in range(self.iter[v], len(self.G[v])):
			self.iter[v] = i
			e = self.G[v][i]
			if e['cap'] > 0 and self.level[v] < self.level[e['to']]:
				d = self.dfs(e['to'], t, min(f, e['cap']))
				if d > 0:
					e['cap'] -= d
					self.G[e['to']][e['rev']]['cap'] += d
					return d
		return 0

	def max_flow(self, s, t):
		flow = 0
		while True:
			self.bfs(s)
			if self.level[t] < 0:
				return flow
			self.iter = [0 for _ in range(self.V)]
			f = self.dfs(s, t, self.inf)
			while f > 0:
				flow += f
				f = self.dfs(s, t, self.inf)

def factrize(n):
	b = 2
	fct = []
	while b * b <= n:
		while n % b == 0:
			n //= b
			if not b in fct:
				fct.append(b)
		b = b + 1
	if n > 1:
		fct.append(n)
	return fct

def gcd(a, b):
	if b == 0:
		return a
	else:
		return gcd(b, a % b)

def lcm(a, b):
	return a // gcd(a, b) * b
while True:
	(m, n) = map(int, readline().split())
	if m == 0 and n == 0:
		break
	network = Dinic(m + n + 2)
	source = 0
	sink = m + n + 1
	blue = []
	red = []
	while len(blue) < m:
		blue += list(map(int, readline().split()))
	while len(red) < n:
		red += list(map(int, readline().split()))
	for i in range(m):
		for j in range(n):
			if gcd(blue[i], red[j]) > 1:
				network.add_edge(i + 1, m + j + 1, 1)
	for i in range(m):
		network.add_edge(source, i + 1, 1)
	for i in range(n):
		network.add_edge(m + i + 1, sink, 1)
	print(network.max_flow(source, sink))


from collections import deque

class Dinic:

	def __init__(self, N):
		self.N = N
		self.G = [[] for i in range(N)]

	def add_edge(self, fr, to, cap):
		forward = [to, cap, None]
		forward[2] = backward = [fr, 0, forward]
		self.G[fr].append(forward)
		self.G[to].append(backward)

	def add_multi_edge(self, v1, v2, cap1, cap2):
		edge1 = [v2, cap1, None]
		edge1[2] = edge2 = [v1, cap2, edge1]
		self.G[v1].append(edge1)
		self.G[v2].append(edge2)

	def bfs(self, s, t):
		self.level = level = [None] * self.N
		deq = deque([s])
		level[s] = 0
		G = self.G
		while deq:
			v = deq.popleft()
			lv = level[v] + 1
			for (w, cap, _) in G[v]:
				if cap and level[w] is None:
					level[w] = lv
					deq.append(w)
		return level[t] is not None

	def dfs(self, v, t, f):
		if v == t:
			return f
		level = self.level
		for e in self.it[v]:
			(w, cap, rev) = e
			if cap and level[v] < level[w]:
				d = self.dfs(w, t, min(f, cap))
				if d:
					e[1] -= d
					rev[1] += d
					return d
		return 0

	def flow(self, s, t):
		flow = 0
		INF = 10 ** 9 + 7
		G = self.G
		while self.bfs(s, t):
			(*self.it,) = map(iter, self.G)
			f = INF
			while f:
				f = self.dfs(s, t, INF)
				flow += f
		return flow

def gcd(a, b):
	while b != 0:
		(a, b) = (b, a % b)
	return a
res = []
while True:
	(m, n) = map(int, input().split())
	if m == 0 and n == 0:
		break
	bl = []
	while len(bl) < m:
		bl.extend(list(map(int, input().split())))
	rl = []
	while len(rl) < n:
		rl.extend(list(map(int, input().split())))
	dinic = Dinic(m + n + 2)
	s = n + m
	t = n + m + 1
	for i in range(m):
		for j in range(n):
			if gcd(bl[i], rl[j]) > 1:
				dinic.add_edge(i, m + j, 1)
	for i in range(m):
		dinic.add_edge(s, i, 1)
	for j in range(m, n + m):
		dinic.add_edge(j, t, 1)
	res.append(dinic.flow(s, t))
for r in res:
	print(r)


from collections import deque

class HopcroftKarp:

	def __init__(self, N0, N1):
		self.N0 = N0
		self.N1 = N1
		self.N = N = 2 + N0 + N1
		self.G = [[] for i in range(N)]
		for i in range(N0):
			forward = [2 + i, 1, None]
			forward[2] = backward = [0, 0, forward]
			self.G[0].append(forward)
			self.G[2 + i].append(backward)
		self.backwards = bs = []
		for i in range(N1):
			forward = [1, 1, None]
			forward[2] = backward = [2 + N0 + i, 0, forward]
			bs.append(backward)
			self.G[2 + N0 + i].append(forward)
			self.G[1].append(backward)

	def add_edge(self, fr, to):
		v0 = 2 + fr
		v1 = 2 + self.N0 + to
		forward = [v1, 1, None]
		forward[2] = backward = [v0, 0, forward]
		self.G[v0].append(forward)
		self.G[v1].append(backward)

	def bfs(self):
		G = self.G
		level = [None] * self.N
		deq = deque([0])
		level[0] = 0
		while deq:
			v = deq.popleft()
			lv = level[v] + 1
			for (w, cap, _) in G[v]:
				if cap and level[w] is None:
					level[w] = lv
					deq.append(w)
		self.level = level
		return level[1] is not None

	def dfs(self, v, t):
		if v == t:
			return 1
		level = self.level
		for e in self.it[v]:
			(w, cap, rev) = e
			if cap and level[v] < level[w] and self.dfs(w, t):
				e[1] = 0
				rev[1] = 1
				return 1
		return 0

	def flow(self):
		flow = 0
		G = self.G
		bfs = self.bfs
		dfs = self.dfs
		while bfs():
			(*self.it,) = map(iter, G)
			while dfs(0, 1):
				flow += 1
		return flow

	def matching(self):
		return [cap for (_, cap, _) in self.backwards]

def gcd(m, n):
	r = m % n
	return gcd(n, r) if r else n
while 1:
	(M, N) = map(int, input().split())
	if M == N == 0:
		break
	B = []
	while len(B) < M:
		B.extend(map(int, input().split()))
	R = []
	while len(R) < N:
		R.extend(map(int, input().split()))
	hk = HopcroftKarp(M, N)
	for i in range(M):
		for j in range(N):
			if gcd(B[i], R[j]) > 1:
				hk.add_edge(i, j)
	print(hk.flow())


import sys
input = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 7)

def gcd(x, y):
	if y == 0:
		return x
	return gcd(y, x % y)

class BipartiteMatching:

	def __init__(self, N, M):
		self.N = N
		self.M = M
		self.pairA = [-1] * N
		self.pairB = [-1] * M
		self.edge = [[] for _ in range(N)]
		self.was = [0] * N
		self.iter = 0

	def add(self, s, t):
		self.edge[s].append(t)

	def _DFS(self, s):
		self.was[s] = self.iter
		for t in self.edge[s]:
			if self.pairB[t] == -1:
				self.pairA[s] = t
				self.pairB[t] = s
				return True
		for t in self.edge[s]:
			if self.was[self.pairB[t]] != self.iter and self._DFS(self.pairB[t]):
				self.pairA[s] = t
				self.pairB[t] = s
				return True
		return False

	def solve(self):
		res = 0
		while True:
			self.iter += 1
			found = 0
			for i in range(self.N):
				if self.pairA[i] == -1 and self._DFS(i):
					found += 1
			if not found:
				break
			res += found
		return res

def inp(num):
	it = (num + 9) // 10
	res = []
	for _ in range(it):
		res.extend(list(map(int, input().split())))
	return res
ans = []
while True:
	(M, N) = map(int, input().split())
	if M == 0 and N == 0:
		break
	match = BipartiteMatching(M, N)
	Blue = inp(M)
	Red = inp(N)
	for (i, b) in enumerate(Blue):
		for (j, r) in enumerate(Red):
			if gcd(b, r) != 1:
				match.add(i, j)
	ans.append(match.solve())
print(*ans, sep='\n')