#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
#define ull unsigned long long
#define poly vector<ll>
#define pb push_back
#define pii pair<int,int>
#define fi first
#define se second
#define mp make_pair
#define For(i,l,r) for(int i=(int)(l);i<=(int)(r);i++)
#define Rep(i,r,l) for(int i=(int)(r);i>=(int)(l);i--)
inline ll read(){
	ll x=0;char ch=getchar();bool d=1;
	for(;!isdigit(ch);ch=getchar()) if(ch=='-') d=0;
	for(;isdigit(ch);ch=getchar()) x=x*10+ch-'0';
	return d?x:-x;
}
inline void write(ll x){
	if(x<0) x=-x,putchar('-');
	if(x>=10) write(x/10);
	putchar('0'+x%10);
}
inline void writeln(ll x){write(x);puts("");}
inline void writep(ll x){write(x);putchar(' ');}
inline ull rnd(){
	return ((ull)rand()<<30^rand())<<4|rand()%4;
}
const int N=2e5+5;
int head[N],opt,sz[N];
struct info{
	int to,nxt;
}e[N<<1];
void add(int x,int y){
	e[++opt]=(info){y,head[x]};head[x]=opt;
	e[++opt]=(info){x,head[y]};head[y]=opt;
}
int mx[N],cmx[N],mn[N];
ll ans;
char s[N];
void dfs1(int u,int fa){
	if(s[u]=='1') mn[u]=0,sz[u]=1;
	else mn[u]=0x3f3f3f3f;
	for(int i=head[u];i;i=e[i].nxt){
		int k=e[i].to;
		if(k==fa) continue;
		dfs1(k,u);sz[u]+=sz[k];
		int t=mx[k]+1;
		if(mx[u]<t) cmx[u]=mx[u],mx[u]=t;
		else cmx[u]=max(cmx[u],t);
		if(sz[k]) mn[u]=min(mn[u],t);
	}
}
void dfs2(int u,int fa){
	int ssw=min(mx[u]-1,cmx[u]+1);
	if(ssw>=mn[u]) ans+=ssw-mn[u]+1;
	for(int i=head[u];i;i=e[i].nxt){
		int k=e[i].to;
		if(k==fa) continue;
		int t=mx[u]==mx[k]+1?cmx[u]+1:mx[u]+1;
		if(mx[k]<t) cmx[k]=mx[k],mx[k]=t;
		else cmx[k]=max(cmx[k],t);
		if(sz[k]<sz[1]) mn[k]=min(mn[k],t);
		dfs2(k,u);
	}
}
int main(){
	int n=read();
	For(i,1,n-1) add(read(),read());
	scanf("%s",s+1);
	dfs1(1,0);dfs2(1,0);
	cout<<ans+1;
}
### Prompt

Your challenge is to write a cpp solution 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<bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
#define ull unsigned long long
#define poly vector<ll>
#define pb push_back
#define pii pair<int,int>
#define fi first
#define se second
#define mp make_pair
#define For(i,l,r) for(int i=(int)(l);i<=(int)(r);i++)
#define Rep(i,r,l) for(int i=(int)(r);i>=(int)(l);i--)
inline ll read(){
	ll x=0;char ch=getchar();bool d=1;
	for(;!isdigit(ch);ch=getchar()) if(ch=='-') d=0;
	for(;isdigit(ch);ch=getchar()) x=x*10+ch-'0';
	return d?x:-x;
}
inline void write(ll x){
	if(x<0) x=-x,putchar('-');
	if(x>=10) write(x/10);
	putchar('0'+x%10);
}
inline void writeln(ll x){write(x);puts("");}
inline void writep(ll x){write(x);putchar(' ');}
inline ull rnd(){
	return ((ull)rand()<<30^rand())<<4|rand()%4;
}
const int N=2e5+5;
int head[N],opt,sz[N];
struct info{
	int to,nxt;
}e[N<<1];
void add(int x,int y){
	e[++opt]=(info){y,head[x]};head[x]=opt;
	e[++opt]=(info){x,head[y]};head[y]=opt;
}
int mx[N],cmx[N],mn[N];
ll ans;
char s[N];
void dfs1(int u,int fa){
	if(s[u]=='1') mn[u]=0,sz[u]=1;
	else mn[u]=0x3f3f3f3f;
	for(int i=head[u];i;i=e[i].nxt){
		int k=e[i].to;
		if(k==fa) continue;
		dfs1(k,u);sz[u]+=sz[k];
		int t=mx[k]+1;
		if(mx[u]<t) cmx[u]=mx[u],mx[u]=t;
		else cmx[u]=max(cmx[u],t);
		if(sz[k]) mn[u]=min(mn[u],t);
	}
}
void dfs2(int u,int fa){
	int ssw=min(mx[u]-1,cmx[u]+1);
	if(ssw>=mn[u]) ans+=ssw-mn[u]+1;
	for(int i=head[u];i;i=e[i].nxt){
		int k=e[i].to;
		if(k==fa) continue;
		int t=mx[u]==mx[k]+1?cmx[u]+1:mx[u]+1;
		if(mx[k]<t) cmx[k]=mx[k],mx[k]=t;
		else cmx[k]=max(cmx[k],t);
		if(sz[k]<sz[1]) mn[k]=min(mn[k],t);
		dfs2(k,u);
	}
}
int main(){
	int n=read();
	For(i,1,n-1) add(read(),read());
	scanf("%s",s+1);
	dfs1(1,0);dfs2(1,0);
	cout<<ans+1;
}
```