#include <bits/stdc++.h>
using namespace std;
#define ull unsigned long long
#define pct __builtin_popcountll
#define eb emplace_back
int n,a[64];string b;vector<ull> vc[64];
priority_queue<ull,vector<ull>,greater<ull>> q;
map<string,bool> vs;unordered_map<ull,ull> dp;
bool chk(ull x)
{
	string t;
	for(int i=0;i<64;++i)
		if(x>>i&1) t+=a[i]+'0';return vs[t];
}
void dfs(int o,ull x)
{
	if(chk(x)) vc[o].eb(x);
	if(pct(x)<4) for(int i=0;i<64;++i) if(x>>i&1)
	{
		if(i%8 && i-1>o && !(x>>i-1&1)) dfs(o,x|(1ull<<i-1));
		if(i%8<7 && i+1>o && !(x>>i+1&1)) dfs(o,x|(1ull<<i+1));
		if(i/8 && i-8>o && !(x>>i-8&1)) dfs(o,x|(1ull<<i-8));
		if(i/8<7 && i+8>o && !(x>>i+8&1)) dfs(o,x|(1ull<<i+8));
	}
}
int main()
{
	ios::sync_with_stdio(0);
	for(int i=0;i<64;++i) cin>>a[i];
	for(int i=1;i<=n;++i) cin>>b,vs[b]=1;
	q.push(0);dp[0]=1;
	for(int i=0;i<64;++i)
	{
		dfs(i,1ull<<i);sort(vc[i].begin(),vc[i].end());
		vc[i].resize(unique(vc[i].begin(),vc[i].end())-vc[i].begin());
	}
	while(!q.empty())
	{
		ull x=q.top();q.pop();
		for(int i=0;i<64;++i) if(!(x>>i&1))
		{
			for(auto j:vc[i]) if(!(x&j))
			{
				ull y=x|j;if(!dp.count(y)) q.push(y);
				dp[y]+=dp[x];
			}
			break;
		}
	}
	printf("%llu\n",dp[(ull)(-1)]);return 0;
}