#include<bits/stdc++.h>
using namespace std;

#define int long long 

#define rep(i,n) for(int i=0;i<(n);i++)
#define pb push_back
#define eb emplace_back
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second
typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;

template<typename A,typename B>inline void chmin(A &a,B b){if(a>b)a=b;}
template<typename A,typename B>inline void chmax(A &a,B b){if(a<b)a=b;}

template<class A,class B>
ostream& operator<<(ostream& ost,const pair<A,B>&p){
	ost<<"{"<<p.first<<","<<p.second<<"}";
	return ost;
}

template<class T>
ostream& operator<<(ostream& ost,const vector<T>&v){
	ost<<"{";
	for(int i=0;i<v.size();i++){
		if(i)ost<<",";
		ost<<v[i];
	}
	ost<<"}";
	return ost;
}

/*
symbol : !"#$%&'()*+,-./
digit : 0~9
symbol2 : :;<=>?@
upper : A~Z
symbol3 : [\]^_`
lower : a~z	
synbol4 : {|}~
*/
struct AhoCorasick{
	//  c \in [OFF,OFF+LEN)
	static const int OFF=(int)('a');
	static const int SUP=(int)('z');
	static const int LEN=SUP-OFF+1;
	struct Node{
		int nex[LEN];
		int failink;
		vector<int>suflist;
		Node():failink(0){memset(nex,-1,sizeof(nex));}
	};
	vector<Node>nds;

	AhoCorasick():nds(1){}

	int process(int k,int c){
		c-=OFF;
		while(nds[k].nex[c]==-1)k=nds[k].failink;
		return nds[k].nex[c];
	}

	void add(const string &s,int id){
		int k=0;
		for(auto c:s){
			c-=OFF;
			if(nds[k].nex[c]==-1){
				nds[k].nex[c]=nds.size();
				nds.emplace_back();
			}
			k=nds[k].nex[c];
		}
		nds[k].suflist.push_back(id);
	}

	void build(){
		queue<int>que;
		for(int i=0;i<LEN;i++){
			if(nds[0].nex[i]==-1)nds[0].nex[i]=0;
			else que.push(nds[0].nex[i]);
		}
		while(que.size()){
			int k=que.front();
			que.pop();
			for(int i=0;i<LEN;i++){
				if(nds[k].nex[i]==-1)continue;
				int nx=nds[k].nex[i];
				nds[nx].failink=process(nds[k].failink,i+OFF);

				vector<int>&curlist=nds[nds[nx].failink].suflist;
				vector<int>&nexlist=nds[nx].suflist;

				nexlist.insert(nexlist.end(),curlist.begin(),curlist.end());
				que.push(nx);
			}
		}
	}
};


signed main(){
	string S;cin>>S;
	int N;cin>>N;
	AhoCorasick ac;
	rep(i,N){
		string s;cin>>s;
		ac.add(s,i);
	}

	ac.build();

	int ans=0;
	int k=0;
	for(auto c:S){
		k=ac.process(k,c);
		if(ac.nds[k].suflist.size()){
			ans++;
			k=0;
		}
	}
	cout<<ans<<endl;
	return 0;
}

### Prompt

Your challenge is to write a cpp solution to the following problem:

G： 検閲により置換 (Censored String)

Problem Statement

You are given the string S, and the set of strings \mathcal P whose size is N. Now we consider applying the following operation to S:

* Choose exactly one character in S, and replace it with '*'.



Let s_i be a i-th character of S, S_{ij} be a consecutive substring in S such that  S = s_i s_{i+1} $\cdots$  s_j, and p_k as the k-th string of P. Your task is to calculate the minimum number of operations for satisfying the following condition.

* For all pairs (S_{ij}, p_k), it is satisfied that S_{ij} \neq p_k.



Input

An input is given in the following format.


S
N
p_1
p_2
$\vdots$
p_N


* In line 1, you are given the string S.
* In line 2, given an integer N. N means the size of P.
* From line 3 to the end, given p_i, the i-th string of P.



Constraints

* 1 \leq |S| \leq 10^5
* 1 \leq N \leq 10^5
* 1 \leq |p_1| + |p_2| +  $\cdots$  + |p_N| \leq 10^5
* If i \neq j, it is guaranteed that p_i \neq p_j
* S, and p_i include lowercase letters only



Output

Print the minimum number of operations in one line.

Sample Input 1


brainfuck
1
fuck


Sample Output 1


1

For example, if you change "brainfuck" into "brainf*ck", you can satisfy the condition. You have to perform operation at least once, and it is the minimum value.

Sample Input 2


aaa
1
a


Sample Output 2


3

You have to operate for all characters.

Sample Input 3


hellshakeyano
3
hell
shake
key


Sample Output 3


2

In this case, for example, if you change "hellshakeyano" into "h*llsha*eyano", you can satisfy the condition. Notice if you replace one character, it might happen that several strings in the set P, which appear as the consecutive substring of S, simultaneously disappear.





Example

Input

brainfuck
1
fuck


Output

1

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;

#define int long long 

#define rep(i,n) for(int i=0;i<(n);i++)
#define pb push_back
#define eb emplace_back
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second
typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;

template<typename A,typename B>inline void chmin(A &a,B b){if(a>b)a=b;}
template<typename A,typename B>inline void chmax(A &a,B b){if(a<b)a=b;}

template<class A,class B>
ostream& operator<<(ostream& ost,const pair<A,B>&p){
	ost<<"{"<<p.first<<","<<p.second<<"}";
	return ost;
}

template<class T>
ostream& operator<<(ostream& ost,const vector<T>&v){
	ost<<"{";
	for(int i=0;i<v.size();i++){
		if(i)ost<<",";
		ost<<v[i];
	}
	ost<<"}";
	return ost;
}

/*
symbol : !"#$%&'()*+,-./
digit : 0~9
symbol2 : :;<=>?@
upper : A~Z
symbol3 : [\]^_`
lower : a~z	
synbol4 : {|}~
*/
struct AhoCorasick{
	//  c \in [OFF,OFF+LEN)
	static const int OFF=(int)('a');
	static const int SUP=(int)('z');
	static const int LEN=SUP-OFF+1;
	struct Node{
		int nex[LEN];
		int failink;
		vector<int>suflist;
		Node():failink(0){memset(nex,-1,sizeof(nex));}
	};
	vector<Node>nds;

	AhoCorasick():nds(1){}

	int process(int k,int c){
		c-=OFF;
		while(nds[k].nex[c]==-1)k=nds[k].failink;
		return nds[k].nex[c];
	}

	void add(const string &s,int id){
		int k=0;
		for(auto c:s){
			c-=OFF;
			if(nds[k].nex[c]==-1){
				nds[k].nex[c]=nds.size();
				nds.emplace_back();
			}
			k=nds[k].nex[c];
		}
		nds[k].suflist.push_back(id);
	}

	void build(){
		queue<int>que;
		for(int i=0;i<LEN;i++){
			if(nds[0].nex[i]==-1)nds[0].nex[i]=0;
			else que.push(nds[0].nex[i]);
		}
		while(que.size()){
			int k=que.front();
			que.pop();
			for(int i=0;i<LEN;i++){
				if(nds[k].nex[i]==-1)continue;
				int nx=nds[k].nex[i];
				nds[nx].failink=process(nds[k].failink,i+OFF);

				vector<int>&curlist=nds[nds[nx].failink].suflist;
				vector<int>&nexlist=nds[nx].suflist;

				nexlist.insert(nexlist.end(),curlist.begin(),curlist.end());
				que.push(nx);
			}
		}
	}
};


signed main(){
	string S;cin>>S;
	int N;cin>>N;
	AhoCorasick ac;
	rep(i,N){
		string s;cin>>s;
		ac.add(s,i);
	}

	ac.build();

	int ans=0;
	int k=0;
	for(auto c:S){
		k=ac.process(k,c);
		if(ac.nds[k].suflist.size()){
			ans++;
			k=0;
		}
	}
	cout<<ans<<endl;
	return 0;
}

```