There is a tree T with N vertices, numbered 1 through N. For each 1 ≤ i ≤ N - 1, the i-th edge connects vertices a_i and b_i.

Snuke is constructing a directed graph T' by arbitrarily assigning direction to each edge in T. (There are 2^{N - 1} different ways to construct T'.)

For a fixed T', we will define d(s,\ t) for each 1 ≤ s,\ t ≤ N, as follows:

* d(s,\ t) = (The number of edges that must be traversed against the assigned direction when traveling from vertex s to vertex t)



In particular, d(s,\ s) = 0 for each 1 ≤ s ≤ N. Also note that, in general, d(s,\ t) ≠ d(t,\ s).

We will further define D as the following:

3d2f3f88e8fa23f065c04cd175c14ebf.png

Snuke is constructing T' so that D will be the minimum possible value. How many different ways are there to construct T' so that D will be the minimum possible value, modulo 10^9 + 7?

Constraints

* 2 ≤ N ≤ 1000
* 1 ≤ a_i,\ b_i ≤ N
* The given graph is a tree.

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}


Output

Print the number of the different ways to construct T' so that D will be the minimum possible value, modulo 10^9 + 7.

Examples

Input

4
1 2
1 3
1 4


Output

2


Input

4
1 2
2 3
3 4


Output

6


Input

6
1 2
1 3
1 4
2 5
2 6


Output

14


Input

10
2 4
2 5
8 3
10 7
1 6
2 8
9 5
8 6
10 6


Output

102
#include<stdio.h>
#include<cstring>
#include<cstdlib>
#include<cmath>
#include<iostream>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<bitset>
#include<utility>
#include<functional>
#include<iomanip>
#include<sstream>
#include<ctime>
#include<cassert>
using namespace std;
#define y0 y0z
#define y1 y1z
#define yn ynz
#define j0 j0z
#define j1 j1z
#define jn jnz
#define tm tmz
#define buli(x) (__builtin_popcountll(x))
#define bur0(x) (__builtin_ctzll(x))
#define bul2(x) (63-__builtin_clzll(x))
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define fil(a,b) memset((a),(b),sizeof(a))
#define cl(a) fil(a,0)
#define siz(x) ((int)(x).size())
#define all(x) (x).begin(),(x).end()
#define foreach(it,a) for(__typeof((a).begin()) it=(a).begin();it!=(a).end();it++)
#define rep(i,a,b) for (int i=(a),_ed=(b);i<_ed;i++)
#define per(i,a,b) for (int i=(b)-1,_ed=(a);i>=_ed;i--)
#define forg(i,gu) for (int i=gu;~i;i=e[i].next)
#define pw(x) ((ll(1))<<(x))
#define upmo(a,b) (((a)=((a)+(b))%mo)<0?(a)+=mo:(a))
#define mmo(a,b) (((a)=1ll*(a)*(b)%mo)<0?(a)+=mo:(a))
void getre(){int x=0;printf("%d\n",1/x);}
void gettle(){int res=1;while(1)res<<=1;printf("%d\n",res);}
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<pii> vpii;
template<typename T,typename S>inline bool upmin(T&a,const S&b){return a>b?a=b,1:0;}
template<typename T,typename S>inline bool upmax(T&a,const S&b){return a<b?a=b,1:0;}
template<typename N,typename PN>inline N flo(N a,PN b){return a>=0?a/b:-((-a-1)/b)-1;}
template<typename N,typename PN>inline N cei(N a,PN b){return a>0?(a-1)/b+1:-(-a/b);}
template<typename N>N gcd(N a,N b){return b?gcd(b,a%b):a;}
template<typename N>inline int sgn(N a){return a>0?1:(a<0?-1:0);}
#if ( ( _WIN32 || __WIN32__ ) && __cplusplus < 201103L)
#define lld "%I64d"
#else
#define lld "%lld"
#endif
inline void gn(long long&x){
	int sg=1;char c;while(((c=getchar())<'0'||c>'9')&&c!='-');c=='-'?(sg=-1,x=0):(x=c-'0');
	while((c=getchar())>='0'&&c<='9')x=x*10+c-'0';x*=sg;
}
inline void gn(int&x){long long t;gn(t);x=t;}
inline void gn(unsigned long long&x){long long t;gn(t);x=t;}
inline void gn(double&x){double t;scanf("%lf",&t);x=t;}
inline void gn(long double&x){double t;scanf("%lf",&t);x=t;}
inline void gs(char *s){scanf("%s",s);}
inline void gc(char &c){while((c=getchar())>126 || c<33);}
inline void pc(char c){putchar(c);}
#ifdef JCVB
#define debug(...) fprintf(stderr, __VA_ARGS__)
#else
#define debug(...)
#endif
typedef long long ll;
typedef double db;
inline ll sqr(ll a){return a*a;}
inline db sqrf(db a){return a*a;}
const int inf=0x3f3f3f3f;
//const ll inf=0x3f3f3f3f3f3f3f3fll;
const db pi=3.14159265358979323846264338327950288L;
const db eps=1e-6;
const int mo=1e9+7;
//int qp(int a,ll b){int n=1;do{if(b&1)n=1ll*n*a%mo;a=1ll*a*a%mo;}while(b>>=1);return n;}


const int TREE_MAXV=3000+5;
struct edge{int v,next;}e[TREE_MAXV*2];int g[TREE_MAXV],etot;
int qu[TREE_MAXV],pre[TREE_MAXV];
int h[33333];
int n;
void ae(int u,int v){
	e[etot].v=v;
	e[etot].next=g[u];g[u]=etot++;
}

int bel[33333];
void bfs(int rt){
	int p=0,q=0;
	pre[rt]=0;
	h[rt]=0;
	qu[q++]=rt;
	while(p!=q){
		int u=qu[p++];
		for (int i=g[u];~i;i=e[i].next)if(e[i].v!=pre[u]){
			pre[e[i].v]=u;
			bel[e[i].v]|=bel[u];
			h[e[i].v]=h[u]+1;
			qu[q++]=e[i].v;
		}
	}
}
void tree_init(){
	static bool ini=0;
	if(!ini){
		ini=1;
		memset(g,-1,sizeof(g));
	}else{
		for (int i=0;i<=n;i++)g[i]=-1;
	}
	etot=0;
}
void readedge(){
	for (int i=1;i<n;i++){
		int x,y;gn(x);gn(y);
		ae(x,y);ae(y,x);
	}
}

int boun[2222],to[2222];
const int zer=1111;
int f[1111][2222];


int dp(){
	cl(f);
	for (int i=n-1;i>=0;i--){
		int u=qu[i];

		for (int j=to[u]-boun[u];j<=to[u]+boun[u];j++){
			f[u][j+zer]=1;
			forg(t,g[u])if(e[t].v!=pre[u])mmo(f[u][j+zer],(f[e[t].v][j-1+zer]+f[e[t].v][j+1+zer]));
		}
	}
	int ret=0;
	rep(t,0,2222)upmo(ret,f[qu[0]][t]);
	return ret;
}

int main()
{
#ifdef JCVB
	//freopen("1.in","r",stdin);
	//freopen("1.out","w",stdout);
	int _time_jc=clock();
#endif
	gn(n);
	tree_init();
	readedge();

	static int dis1[2222];

	bfs(1);
	int ma=1;
	rep(u,2,n+1)if(h[u]>h[ma])ma=u;
	bfs(ma);
	int mav=1;
	rep(u,1,n+1)if(h[u]>h[mav])mav=u;

	bfs(mav);
	rep(i,1,n+1)dis1[i]=h[i];
	bfs(ma);
	int r;

	r=cei(h[mav],2);
	int rt=0,rt2=0;

	if(h[mav]%2==0){
		rep(i,1,n+1){
			if(dis1[i]==h[i] && h[i]==h[mav]/2)rt=i;
		}
	}else{
		rep(i,1,n+1){
			if(dis1[i]==h[mav]/2 && h[i]==(h[mav]+1)/2)rt=i;
			if(dis1[i]==(h[mav]+1)/2 && h[i]==(h[mav]+0)/2)rt2=i;
		}
	}

	bel[rt2]=1;
	bfs(rt);


	int ans=0;
	if(rt2==0){
		rep(u,1,n+1)boun[u]=r-h[u],to[u]=0;
		upmo(ans,dp());
	}else{
		rep(u,1,n+1){
			int d;
			if(!bel[u])d=r-1-h[u];else d=r-h[u];
			if(bel[u]){
				to[u]=0;
				boun[u]=d;
			}else{
				to[u]=0;
				boun[u]=d+1;
			}
		}
		upmo(ans,dp());
		/* rep(u,1,n+1){ */
		/* 	int d; */
		/* 	if(!bel[u])d=r-1-h[u];else d=r-h[u]; */
		/* 	if(bel[u]){ */
		/* 		to[u]=0; */
		/* 		boun[u]=d; */
		/* 	}else{ */
		/* 		to[u]=0; */
		/* 		boun[u]=d+1; */
		/* 		if(d==0){ */
		/* 			to[u]=1; */
		/* 			boun[u]=0; */
		/* 		} */
		/* 	} */
		/* } */
		/* upmo(ans,-dp()); */

		/* rep(u,1,n+1){ */
		/* 	int d; */
		/* 	if(!bel[u])d=r-1-h[u];else d=r-h[u]; */
		/* 	if(bel[u]){ */
		/* 		to[u]=0; */
		/* 		boun[u]=d; */
		/* 	}else{ */
		/* 		to[u]=0; */
		/* 		boun[u]=d+1; */
		/* 		if(d==0){ */
		/* 			to[u]=-1; */
		/* 			boun[u]=0; */
		/* 		} */
		/* 	} */
		/* } */
		/* upmo(ans,-dp()); */

		rep(u,1,n+1){
			int d;
			if(!bel[u])d=r-1-h[u];else d=r-h[u];
			if(bel[u]){
				to[u]=0;
				boun[u]=d+1;
			}else{
				to[u]=0;
				boun[u]=d;
			}
		}
		upmo(ans,dp());

		rep(u,1,n+1){
			int d;
			if(!bel[u])d=r-1-h[u];else d=r-h[u];
			if(!bel[u]){
				to[u]=0;
				boun[u]=d;
			}else{
				to[u]=0;
				boun[u]=d+1;
				if(d==0){
					to[u]=1;
					boun[u]=0;
				}
			}
		}
		//upmo(ans,-dp());

		rep(u,1,n+1){
			int d;
			if(!bel[u])d=r-1-h[u];else d=r-h[u];
			if(!bel[u]){
				to[u]=0;
				boun[u]=d;
			}else{
				to[u]=0;
				boun[u]=d+1;
				if(d==0){
					to[u]=-1;
					boun[u]=0;
				}
			}
		}
		//upmo(ans,-dp());
		/* rep(u,1,n+1){ */
		/* 	int d; */
		/* 	if(!bel[u])d=r-1-h[u];else d=r-h[u]; */
		/* 	if(!bel[u]){ */
		/* 		to[u]=1; */
		/* 		boun[u]=d+1; */
		/* 		if(d==0){ */
		/* 			to[u]=0; */
		/* 			boun[u]=0; */
		/* 		} */
		/* 	}else{ */
		/* 		to[u]=0; */
		/* 		boun[u]=d+1; */
		/* 		if(d==0){ */
		/* 			to[u]=1; */
		/* 			boun[u]=0; */
		/* 		} */
		/* 	} */
		/* } */
		/* upmo(ans,dp()); */
		/* rep(u,1,n+1){ */
		/* 	int d; */
		/* 	if(!bel[u])d=r-1-h[u];else d=r-h[u]; */
		/* 	if(bel[u]){ */
		/* 		to[u]=1; */
		/* 		boun[u]=d+1; */
		/* 		if(d==0){ */
		/* 			to[u]=0; */
		/* 			boun[u]=0; */
		/* 		} */
		/* 	}else{ */
		/* 		to[u]=0; */
		/* 		boun[u]=d+1; */
		/* 		if(d==0){ */
		/* 			to[u]=1; */
		/* 			boun[u]=0; */
		/* 		} */
		/* 	} */
		/* } */
		/* upmo(ans,dp()); */
		rep(u,1,n+1){
			int d;
			if(!bel[u])d=r-1-h[u];else d=r-h[u];
			if(!bel[u]){
				to[u]=0;
				boun[u]=d;
			}else{
				to[u]=1;
				boun[u]=d;
			}
		}
		upmo(ans,-dp());
		rep(u,1,n+1){
			int d;
			if(!bel[u])d=r-1-h[u];else d=r-h[u];
			if(bel[u]){
				to[u]=0;
				boun[u]=d;
			}else{
				to[u]=1;
				boun[u]=d;
			}
		}
		upmo(ans,-dp());
	}

	printf("%d\n",ans);
#ifdef JCVB
	debug("time: %d\n",int(clock()-_time_jc));
#endif
	return 0;
}


