Code

#include<bits/stdc++.h>
using namespace std;
const int N=1000002;
struct node{
	int to,ne;
}e[N<<1];
int sz[N],x,y,tot,h[N],num[N],n,i,cnt,ans,j;
inline char gc(){
	static char buf[100000],*p1=buf,*p2=buf;
	return p1==p2&&(p2=(p1=buf)+fread(buf,1,100000,stdin),p1==p2)?EOF:*p1++;
}
inline int rd(){
	int x=0,fl=1;char ch=gc();
	for (;ch<48||ch>57;ch=gc())if(ch=='-')fl=-1;
	for (;48<=ch&&ch<=57;ch=gc())x=(x<<3)+(x<<1)+(ch^48);
	return x*fl;
}
inline void wri(int a){if(a<0)a=-a,putchar('-');if(a>=10)wri(a/10);putchar(a%10|48);}
inline void wln(int a){wri(a);puts("");}
void add(int x,int y){e[++tot]=(node){y,h[x]},h[x]=tot;}
void dfs(int u,int fa){
	sz[u]=1;
	for (int i=h[u],v;i;i=e[i].ne)
		if ((v=e[i].to)!=fa) dfs(v,u),sz[u]+=sz[v];
}
int main(){
	n=rd();
	for (i=1;i<n;i++) x=rd(),y=rd(),add(x,y),add(y,x);
	dfs(1,0);
	for (i=1;i<=n;i++) num[sz[i]]++;
	for (i=1;i<=n;i++)
		if (n%i==0){
			cnt=0;
			for (j=1;j<=n/i;j++) cnt+=num[i*j];
			ans+=cnt==n/i;
		}
	printf("%d",ans);
}