#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
#include<vector>
#include<queue>
#include<map>
#include<bitset>
#include<set>
#define N (200010)
#define P ()
#define M (N<<1)
#define inf (0x7f7f7f7f)
#define rg register int
#define Label puts("NAIVE")
#define spa print(' ')
#define ent print('\n')
#define rand() (((rand())<<(15))^(rand()))
#define file(s) freopen(s".in","r",stdin),freopen(s".out","w",stdout)
typedef long double ld;
typedef long long LL;
typedef unsigned long long ull;
using namespace std;
namespace fastIO1{
	inline char read(){
		static const int IN_LEN=1000000;
		static char buf[IN_LEN],*s,*t;
		return (s==t?t=(s=buf)+fread(buf,1,IN_LEN,stdin),(s==t?-1:*s++):*s++);
	}
	template<class T>
	inline void read(T &x){
		static bool iosig;
		static char c;
		for(iosig=false,c=read();!isdigit(c);c=read()){
			if(c=='-')iosig=true;
			if(c==-1)return;
		}
		for(x=0;isdigit(c);c=read())x=((x+(x<<2))<<1)+(c^'0');
		if(iosig)x=-x;
	}
	inline char readc(char &c){
		for(c=read();!isalpha(c)&&!isdigit(c);c=read())
		if(c==-1)return 0;
	}
	const int OUT_LEN = 10000000;
	char obuf[OUT_LEN],*ooh=obuf;
	inline void print(char c) {
		if(ooh==obuf+OUT_LEN)fwrite(obuf,1,OUT_LEN,stdout),ooh=obuf;
		*ooh++=c;
	}
	template<class T>
	inline void print(T x){
		static int buf[30],cnt;
		if(x==0)print('0');
		else{
			if(x<0)print('-'),x=-x;
			for(cnt=0;x;x/=10)buf[++cnt]=x%10+48;
			while(cnt)print((char)buf[cnt--]);
		}
	}
	inline void flush(){fwrite(obuf,1,ooh-obuf,stdout);}
}
namespace fastIO2{
	template<class T>
	inline void read(T &x){
		static bool iosig;
		static char c;
		for(iosig=false,c=getchar();!isdigit(c);c=getchar()){
			if(c=='-')iosig=true;
			if(c==-1)return;
		}
		for(x=0;isdigit(c);c=getchar())x=((x+(x<<2))<<1)+(c^'0');
		if(iosig)x=-x;
	}
}
using namespace fastIO1;
int n,E,fi[N],ne[M],b[M]; char str[N];
int f[N],sf[N],siz[N],mn[N]; LL ans;
void add(int x,int y){
	ne[++E]=fi[x],fi[x]=E,b[E]=y;
}
void dfs1(int u,int pre){
//	cout<<u<<endl;
	if(str[u]=='1')mn[u]=0,siz[u]=1;
	else mn[u]=inf;
	for(int i=fi[u];i;i=ne[i]){
		int v=b[i];
		if(v==pre)continue;dfs1(v,u),siz[u]+=siz[v];
		if(f[v]+1>f[u])sf[u]=f[u],f[u]=f[v]+1;
		else sf[u]=max(sf[u],f[v]+1);
		if(siz[v])mn[u]=min(mn[u],f[v]+1);
	}
}
void dfs2(int u,int pre){
//	cout<<u<<endl;
	int tmp=min(f[u]-1,sf[u]+1);
	if(tmp>=mn[u])ans+=(LL)tmp-mn[u]+1;
//	cout<<tmp<<" "<<u<<" "<<mn[u]<<endl;
	for(int i=fi[u];i;i=ne[i]){
		int v=b[i]; if(v==pre)continue;
		int len=(f[u]==f[v]+1)?sf[u]+1:f[u]+1;
		if(f[v]<len)sf[v]=f[v],f[v]=len;
        else sf[v]=max(sf[v],len);
        if(siz[v]<siz[1])mn[v]=min(mn[v],len);
        dfs2(v,u);
	}
}
int main(){
	read(n);
	for(int i=1;i<n;i++){
		int x,y;
		read(x),read(y);
		add(x,y),add(y,x);
	}
	for(int i=1;i<=n;i++)readc(str[i]);
	dfs1(1,0),dfs2(1,0);
	cout<<ans+1;
}
### Prompt

In CPP, your task is to solve the following problem:

There is a tree with N vertices. The vertices are numbered 1 through N. For each 1 ≤ i ≤ N - 1, the i-th edge connects vertices a_i and b_i. The lengths of all the edges are 1.

Snuke likes some of the vertices. The information on his favorite vertices are given to you as a string s of length N. For each 1 ≤ i ≤ N, s_i is `1` if Snuke likes vertex i, and `0` if he does not like vertex i.

Initially, all the vertices are white. Snuke will perform the following operation exactly once:

* Select a vertex v that he likes, and a non-negative integer d. Then, paint all the vertices black whose distances from v are at most d.



Find the number of the possible combinations of colors of the vertices after the operation.

Constraints

* 2 ≤ N ≤ 2×10^5
* 1 ≤ a_i, b_i ≤ N
* The given graph is a tree.
* |s| = N
* s consists of `0` and `1`.
* s contains at least one occurrence of `1`.

Input

The input is given from Standard Input in the following format:


N
a_1 b_1
a_2 b_2
:
a_{N - 1} b_{N - 1}
s


Output

Print the number of the possible combinations of colors of the vertices after the operation.

Examples

Input

4
1 2
1 3
1 4
1100


Output

4


Input

5
1 2
1 3
1 4
4 5
11111


Output

11


Input

6
1 2
1 3
1 4
2 5
2 6
100011


Output

8

### Response

```cpp
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
#include<vector>
#include<queue>
#include<map>
#include<bitset>
#include<set>
#define N (200010)
#define P ()
#define M (N<<1)
#define inf (0x7f7f7f7f)
#define rg register int
#define Label puts("NAIVE")
#define spa print(' ')
#define ent print('\n')
#define rand() (((rand())<<(15))^(rand()))
#define file(s) freopen(s".in","r",stdin),freopen(s".out","w",stdout)
typedef long double ld;
typedef long long LL;
typedef unsigned long long ull;
using namespace std;
namespace fastIO1{
	inline char read(){
		static const int IN_LEN=1000000;
		static char buf[IN_LEN],*s,*t;
		return (s==t?t=(s=buf)+fread(buf,1,IN_LEN,stdin),(s==t?-1:*s++):*s++);
	}
	template<class T>
	inline void read(T &x){
		static bool iosig;
		static char c;
		for(iosig=false,c=read();!isdigit(c);c=read()){
			if(c=='-')iosig=true;
			if(c==-1)return;
		}
		for(x=0;isdigit(c);c=read())x=((x+(x<<2))<<1)+(c^'0');
		if(iosig)x=-x;
	}
	inline char readc(char &c){
		for(c=read();!isalpha(c)&&!isdigit(c);c=read())
		if(c==-1)return 0;
	}
	const int OUT_LEN = 10000000;
	char obuf[OUT_LEN],*ooh=obuf;
	inline void print(char c) {
		if(ooh==obuf+OUT_LEN)fwrite(obuf,1,OUT_LEN,stdout),ooh=obuf;
		*ooh++=c;
	}
	template<class T>
	inline void print(T x){
		static int buf[30],cnt;
		if(x==0)print('0');
		else{
			if(x<0)print('-'),x=-x;
			for(cnt=0;x;x/=10)buf[++cnt]=x%10+48;
			while(cnt)print((char)buf[cnt--]);
		}
	}
	inline void flush(){fwrite(obuf,1,ooh-obuf,stdout);}
}
namespace fastIO2{
	template<class T>
	inline void read(T &x){
		static bool iosig;
		static char c;
		for(iosig=false,c=getchar();!isdigit(c);c=getchar()){
			if(c=='-')iosig=true;
			if(c==-1)return;
		}
		for(x=0;isdigit(c);c=getchar())x=((x+(x<<2))<<1)+(c^'0');
		if(iosig)x=-x;
	}
}
using namespace fastIO1;
int n,E,fi[N],ne[M],b[M]; char str[N];
int f[N],sf[N],siz[N],mn[N]; LL ans;
void add(int x,int y){
	ne[++E]=fi[x],fi[x]=E,b[E]=y;
}
void dfs1(int u,int pre){
//	cout<<u<<endl;
	if(str[u]=='1')mn[u]=0,siz[u]=1;
	else mn[u]=inf;
	for(int i=fi[u];i;i=ne[i]){
		int v=b[i];
		if(v==pre)continue;dfs1(v,u),siz[u]+=siz[v];
		if(f[v]+1>f[u])sf[u]=f[u],f[u]=f[v]+1;
		else sf[u]=max(sf[u],f[v]+1);
		if(siz[v])mn[u]=min(mn[u],f[v]+1);
	}
}
void dfs2(int u,int pre){
//	cout<<u<<endl;
	int tmp=min(f[u]-1,sf[u]+1);
	if(tmp>=mn[u])ans+=(LL)tmp-mn[u]+1;
//	cout<<tmp<<" "<<u<<" "<<mn[u]<<endl;
	for(int i=fi[u];i;i=ne[i]){
		int v=b[i]; if(v==pre)continue;
		int len=(f[u]==f[v]+1)?sf[u]+1:f[u]+1;
		if(f[v]<len)sf[v]=f[v],f[v]=len;
        else sf[v]=max(sf[v],len);
        if(siz[v]<siz[1])mn[v]=min(mn[v],len);
        dfs2(v,u);
	}
}
int main(){
	read(n);
	for(int i=1;i<n;i++){
		int x,y;
		read(x),read(y);
		add(x,y),add(y,x);
	}
	for(int i=1;i<=n;i++)readc(str[i]);
	dfs1(1,0),dfs2(1,0);
	cout<<ans+1;
}
```