Problem: We have a tree G with N vertices numbered 1 to N. The i-th edge of G connects Vertex a_i and Vertex b_i.

Consider adding zero or more edges in G, and let H be the graph resulted.

Find the number of graphs H that satisfy the following conditions, modulo 998244353.

* H does not contain self-loops or multiple edges.
* The diameters of G and H are equal.
* For every pair of vertices in H that is not directly connected by an edge, the addition of an edge directly connecting them would reduce the diameter of the graph.

Constraints

* 3 \le N \le 2 \times 10^5
* 1 \le a_i, b_i \le N
* The given graph is a tree.

Input

Input is given from Standard Input in the following format:


N
a_1 b_1
\vdots
a_{N-1} b_{N-1}


Output

Print the answer.

Examples

Input

6
1 6
2 1
5 2
3 4
2 3


Output

3


Input

3
1 2
2 3


Output

1


Input

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


Output

27


Input

19
2 4
15 8
1 16
1 3
12 19
1 18
7 11
11 15
12 9
1 6
7 14
18 2
13 12
13 5
16 13
7 1
11 10
7 17


Output

78732

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;

typedef long long lint;
typedef long double louble;

template<typename T1,typename T2> inline T1 max(T1 a,T2 b){return a<b?b:a;}
template<typename T1,typename T2> inline T1 min(T1 a,T2 b){return a<b?a:b;}

const char lf = '\n';

namespace ae86
{
	const int bufl = 1 << 15;

	char buf[bufl],*s=buf,*t=buf;

	inline int fetch()
	{
		if(s==t){t=(s=buf)+fread(buf,1,bufl,stdin);if(s==t)return EOF;}
		return *s++;
	}

	inline int ty()
	{
		int a=0;int b=1,c=fetch();
		while(!isdigit(c))b^=c=='-',c=fetch();
		while(isdigit(c))a=a*10+c-48,c=fetch();
		return b?a:-a;
	}
}
using ae86::ty;

const int _ = 200007 , mo = 998244353;

template<typename T1,typename T2> inline T1 ad(T1 &a,T2 b){return a=a+b>=mo?a+b-mo:a+b;}
template<typename T1,typename T2> inline T1 dl(T1 &a,T2 b){return a=a>=b?a-b:a-b+mo;}
template<typename T1,typename T2> inline T1 add(T1 a,T2 b){return a+b>=mo?a+b-mo:a+b;}
template<typename T1,typename T2> inline T1 del(T1 a,T2 b){return a>=b?a-b:a-b+mo;}

lint powa(lint a,lint t)
{
	lint b=1;a=(a+mo)%mo;
	while(t){if(t&1)b=b*a%mo;a=a*a%mo,t>>=1;}
	return b;
}

inline lint inva(lint a)
{
	return powa(a,mo-2);
}

vector<int> e[_];

int n,fa[_]={0},rt=0,mxdep=0;

void dfs(int x,int ff,int dep)
{
	fa[x]=ff;
	if(dep>mxdep)mxdep=dep,rt=x;
	for(auto b:e[x])if(b!=ff)dfs(b,x,dep+1);
}

int ps[_]={0},lps=0;
lint f[_][3][3]={0};

void dfs2(int x,int ff,int dep)
{
	fa[x]=ff;
	memset(f[x],0,sizeof(f[x]));
	if(dep==lps/2)f[x][1][1]=1;
	else f[x][0][0]=1;

	for(auto b:e[x])
	{
		if(b==ff)continue;
		dfs2(b,x,dep+1);
		lint sf[3][3];memset(sf,0,sizeof(sf));
		for(int i=0;i<3;i++)
			for(int j=0;j<3;j++)
				for(int p=0;p<3;p++)
					for(int q=0;q<3;q++)
						for(int r=-1;r<=1;r++)
						{
							int pp=r==1?p:0,qq=r==-1?q:0;
							pp=min(2,pp+i),qq=min(2,qq+j);
							ad(sf[pp][qq],f[x][i][j]*f[b][p][q]%mo);
						}
		memcpy(f[x],sf,sizeof(sf));
	}
}

int main()
{
	ios::sync_with_stdio(0),cout.tie(nullptr);

	n=ty();
	for(int i=1,a,b;i<n;i++)a=ty(),b=ty(),e[a].emplace_back(b),e[b].emplace_back(a);

	dfs(1,0,1),mxdep=0,dfs(rt,0,1);
	for(int i=rt;i;i=fa[i])ps[++lps]=i;

	if(lps&1)
	{
		int mid=ps[lps/2+1];
		dfs2(mid,0,0);
		cout<<f[mid][1][1]*inva(2)%mo<<lf;
		return 0;
	}
	
	int ll=ps[lps/2],rr=ps[lps/2+1];
	dfs2(ll,rr,1),dfs2(rr,ll,1);
	cout<<add(add(f[ll][1][0],f[ll][1][1]),f[ll][1][2])
		*add(add(f[rr][0][1],f[rr][1][1]),f[rr][2][1])%mo<<lf;

	return 0;
}