#include<set>
#include<map>
#include<cmath>
#include<queue>
#include<bitset>
#include<string>
#include<cstdio>
#include<cctype>
#include<cassert>
#include<cstdlib>
#include<cstring>
#include<sstream>
#include<iostream>
#include<algorithm>

#define For(i,x,y) for (int i=x;i<y;i++)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define lf else if

#define dprintf(...) fprintf(stderr,__VA_ARGS__)
using namespace std;

typedef long long ll;
typedef double db;
typedef pair<int,int> pii;
typedef vector<int> Vi;

int IN(){
	int c,f,x;
	while (!isdigit(c=getchar())&&c!='-');c=='-'?(f=1,x=0):(f=0,x=c-'0');
	while (isdigit(c=getchar())) x=(x<<1)+(x<<3)+c-'0';return !f?x:-x;
}

const int N=200000+19;
const int oo=(1<<30)-1;

struct Edge{
	int y,nxt;
} E[N*2];
Vi V[N];
int D[N],U[N],top[N],low[N],A[N],B[N];
int n;
char s[N];
ll ans;

void Link(int x,int y){
	V[x].pb(y);
	V[y].pb(x);
}
void dfs(int x,int fa){
	int y;
	A[x]=(s[x]=='1');
	For(i,0,V[x].size()) if ((y=V[x][i])!=fa){
		dfs(y,x);
		D[x]=max(D[x],D[y]+1);
		A[x]|=A[y];
	}
}
void dfs2(int x,int fa){
	int mx=U[x],tmp=B[x]|(s[x]=='1');
	for (int y:V[x]) if (y!=fa){
		B[y]|=tmp;
		U[y]=max(U[y],mx+1);
		mx=max(mx,D[y]+1);
		tmp|=A[y];
	}
	mx=U[x],tmp=B[x]|(s[x]=='1');
	for (int i=int(V[x].size())-1,y;~i;i--) if ((y=V[x][i])!=fa){
		B[y]|=tmp;
		U[y]=max(U[y],mx+1);
		mx=max(mx,D[y]+1);
		tmp|=A[y];
	}
	for (int y:V[x]) if (y!=fa) dfs2(y,x);
}
void calc(int x,int fa){
	Vi T;
	top[x]=max(D[x],U[x])-1;
	low[x]=n;
	T.pb(-1);
	if (~fa){
		T.pb(U[x]-1);
		if (B[x]) low[x]=min(low[x],U[x]);
	}
	for (int y:V[x]) if (y!=fa){
		T.pb(D[y]);
		if (A[y]) low[x]=min(low[x],D[y]+1);
		calc(y,x);
	}
	sort(T.begin(),T.end(),greater<int>());
	top[x]=min(top[x],T[1]+2);
}

int main(){
	n=IN();
	For(i,1,n) Link(IN(),IN());
	scanf("%s",s+1);
	if (n==1){
		puts("1");
		return 0;
	}
	dfs(1,-1);
	dfs2(1,-1);
	calc(1,-1);
	For(i,1,n+1)
		if (s[i]=='1'){
			ans+=max(top[i]+1,0);
		} else{
			ans+=max(top[i]-max(low[i],1)+1,0);
		}
	ans++;
	cout<<ans<<endl;
}
### Prompt

Please create a solution in cpp to 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<set>
#include<map>
#include<cmath>
#include<queue>
#include<bitset>
#include<string>
#include<cstdio>
#include<cctype>
#include<cassert>
#include<cstdlib>
#include<cstring>
#include<sstream>
#include<iostream>
#include<algorithm>

#define For(i,x,y) for (int i=x;i<y;i++)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define lf else if

#define dprintf(...) fprintf(stderr,__VA_ARGS__)
using namespace std;

typedef long long ll;
typedef double db;
typedef pair<int,int> pii;
typedef vector<int> Vi;

int IN(){
	int c,f,x;
	while (!isdigit(c=getchar())&&c!='-');c=='-'?(f=1,x=0):(f=0,x=c-'0');
	while (isdigit(c=getchar())) x=(x<<1)+(x<<3)+c-'0';return !f?x:-x;
}

const int N=200000+19;
const int oo=(1<<30)-1;

struct Edge{
	int y,nxt;
} E[N*2];
Vi V[N];
int D[N],U[N],top[N],low[N],A[N],B[N];
int n;
char s[N];
ll ans;

void Link(int x,int y){
	V[x].pb(y);
	V[y].pb(x);
}
void dfs(int x,int fa){
	int y;
	A[x]=(s[x]=='1');
	For(i,0,V[x].size()) if ((y=V[x][i])!=fa){
		dfs(y,x);
		D[x]=max(D[x],D[y]+1);
		A[x]|=A[y];
	}
}
void dfs2(int x,int fa){
	int mx=U[x],tmp=B[x]|(s[x]=='1');
	for (int y:V[x]) if (y!=fa){
		B[y]|=tmp;
		U[y]=max(U[y],mx+1);
		mx=max(mx,D[y]+1);
		tmp|=A[y];
	}
	mx=U[x],tmp=B[x]|(s[x]=='1');
	for (int i=int(V[x].size())-1,y;~i;i--) if ((y=V[x][i])!=fa){
		B[y]|=tmp;
		U[y]=max(U[y],mx+1);
		mx=max(mx,D[y]+1);
		tmp|=A[y];
	}
	for (int y:V[x]) if (y!=fa) dfs2(y,x);
}
void calc(int x,int fa){
	Vi T;
	top[x]=max(D[x],U[x])-1;
	low[x]=n;
	T.pb(-1);
	if (~fa){
		T.pb(U[x]-1);
		if (B[x]) low[x]=min(low[x],U[x]);
	}
	for (int y:V[x]) if (y!=fa){
		T.pb(D[y]);
		if (A[y]) low[x]=min(low[x],D[y]+1);
		calc(y,x);
	}
	sort(T.begin(),T.end(),greater<int>());
	top[x]=min(top[x],T[1]+2);
}

int main(){
	n=IN();
	For(i,1,n) Link(IN(),IN());
	scanf("%s",s+1);
	if (n==1){
		puts("1");
		return 0;
	}
	dfs(1,-1);
	dfs2(1,-1);
	calc(1,-1);
	For(i,1,n+1)
		if (s[i]=='1'){
			ans+=max(top[i]+1,0);
		} else{
			ans+=max(top[i]-max(low[i],1)+1,0);
		}
	ans++;
	cout<<ans<<endl;
}
```