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;
/*#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<typename T> using gpp_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T, typename L> using gpp_map = tree<T, L, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T> using gpp_multiset = tree<T, null_type, less_equal<T>, rb_tree_tag, tree_order_statistics_node_update>;*/
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin);i<(end);i++)
#define REP(i, n) FOR(i,0,n)
#define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--)
#define IREP(i, n) IFOR(i,0,n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(),v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL<<(n))
#define bit_exist(x, n) ((x >> n) & 1)
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v) { cout << #v << "=" << endl; REP(i_debug, v.size()){ cout << v[i_debug] << ","; } cout << endl; }
#define mdebug(m) { cout << #m << "=" << endl; REP(i_debug, m.size()){ REP(j_debug, m[i_debug].size()){ cout << m[i_debug][j_debug] << ","; } cout << endl;} }
#define Return(ans) { cout << (ans) << endl; return 0; }
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for (auto &x : v) is >> x; return is; }
template<typename T> ostream &operator<<(ostream &os, vector<T> &v){ for(int i = 0; i < v.size(); i++) { cout << v[i]; if(i != v.size() - 1) cout << endl; }; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, pair<T1, T2> p){ cout << '(' << p.first << ',' << p.second << ')'; return os; }
template<typename T> void Out(T x) { cout << x << endl; }
template<typename T1, typename T2> void Ans(bool f, T1 y, T2 n) { if(f) Out(y); else Out(n); }

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

//int dx[4] = {1,0,-1,0};
//int dy[4] = {0,1,0,-1};
//char d[4] = {'D','R','U','L'};

//const int mod = 1000000007;
const int mod = 998244353;
//#define Add(x, y) x = (x + (y)) % mod
//#define Mult(x, y) x = (x * (y)) % mod

template<long long MOD>
struct ModInt{

    using ll = long long;
    ll val;

    void setval(ll v) { val = v % MOD; };
    ModInt(): val(0) {}
    ModInt(ll v) { setval(v); };

    ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); }
    ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); }
    ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); }
    ModInt operator/(const ModInt &x) const { return *this * x.inv(); }
    ModInt operator-() const { return ModInt(MOD - val); }
    ModInt operator+=(const ModInt &x) { return *this = *this + x; }
    ModInt operator-=(const ModInt &x) { return *this = *this - x; }
    ModInt operator*=(const ModInt &x) { return *this = *this * x; }
    ModInt operator/=(const ModInt &x) { return *this = *this / x; }

    friend ostream& operator<<(ostream &os, const ModInt &x) { os << x.val; return os; }
    friend istream& operator>>(istream &is, ModInt &x) { is >> x.val; x.val = (x.val % MOD + MOD) % MOD; return is; }

    ModInt pow(ll n) const {
        ModInt a = 1;
        if(n == 0) return a;
        int i0 = 64 - __builtin_clzll(n);
        for(int i = i0 - 1; i >= 0; i--){
            a = a * a;
            if((n >> i) & 1) a *= (*this); 
        }
        return a;
    }
    ModInt inv() const { return this->pow(MOD - 2); }
};

using mint = ModInt<mod>; mint pow(mint x, long long n) { return x.pow(n); }
//using mint = double; //for debug
using mvec = vector<mint>;
using mmat = vector<mvec>;

struct Combination{

    vector<mint> fact, invfact;

    Combination(int N){
        fact = vector<mint>({mint(1)});
        invfact = vector<mint>({mint(1)});
        fact_initialize(N);
    }

    void fact_initialize(int N){
        int i0 = fact.size();
        if(i0 >= N + 1) return;
        fact.resize(N + 1);
        invfact.resize(N + 1);
        for(int i = i0; i <= N; i++) fact[i] = fact[i - 1] * i;
        invfact[N] = (mint)1 / fact[N];
        for(int i = N - 1; i >= i0; i--) invfact[i] = invfact[i + 1] * (i + 1); 
    }

    mint nCr(int n, int r){
        if(n < 0 || r < 0 || r > n) return mint(0);
        if(fact.size() < n + 1) fact_initialize(n);
        return fact[n] * invfact[r] * invfact[n - r];
    }

    mint nPr(int n, int r){
        if(n < 0 || r < 0 || r > n) return mint(0);
        if(fact.size() < n + 1) fact_initialize(n);
        return fact[n] * invfact[n - r];
    }

};

struct edge{int to, cost, id;};

class Graph
{
public:
    int N;
    vector<vector<edge>> G;
    bools f;
    mmat dp;

    Graph(int N): N(N){
        G = vector<vector<edge>>(N, vector<edge>(0));
        f = bools(N, false);
        dp = mmat(N, mvec(3, 0));
    }

    void add_Directed_edge(int from, int to, int cost = 1, int id = 0){
        G[from].push_back(edge({to, cost, id}));
    }

    void add_Undirected_edge(int v1, int v2, int cost = 1, int id = 0){
        add_Directed_edge(v1, v2, cost, id);
        add_Directed_edge(v2, v1, cost, id);
    }

    //calculate diameter of a Tree
    void dfs_for_calcdist(int v, int p, int c, vec &dist){
        if(p != -1) dist[v] = dist[p] + c;
        for(auto e: G[v]) if(e.to != p) dfs_for_calcdist(e.to, v, e.cost, dist);
    } 

    int diameter(int &v1, int &v2, int s = 0){
        vec dist(N, 0);
        dfs_for_calcdist(s, -1, -1, dist);
        v1 = distance(dist.begin(), max_element(dist.begin(), dist.end()));
        fill(dist.begin(), dist.end(), 0);
        dfs_for_calcdist(v1, -1, -1, dist);
        auto amax = max_element(dist.begin(), dist.end());
        v2 = distance(dist.begin(), amax);
        return *amax;
    }

    void dfs(int v, int p){

        if(f[v]) dp[v][1] = 1;
        else dp[v][0] = 1;

        if(p != -1){
            for(auto e: G[v]) if(e.to != p){
                dfs(e.to, v);
                mvec tmp(3, 0);
                tmp[0] = dp[v][0] * (dp[e.to][0] * 3 + dp[e.to][1] * 2 + dp[e.to][2] * 2);
                tmp[1] = dp[v][0] * dp[e.to][1] + dp[v][1] * (dp[e.to][0] * 3 + dp[e.to][1] * 2 + dp[e.to][2] * 2);
                tmp[2] = dp[v][1] * dp[e.to][1] + dp[v][2] * (dp[e.to][0] + dp[e.to][1] + dp[e.to][2]) * 3 + (dp[v][0] + dp[v][1]) * dp[e.to][2];
                dp[v] = tmp;
            }
        }else{
            dp[v] = mvec(4, 0);
            dp[v][0] = 1;
            for(auto e: G[v]) if(e.to != p){
                dfs(e.to, v);
                mvec tmp(4, 0);
                REP(j, 4){
                    tmp[j] += dp[v][j] * (dp[e.to][0] * 3 + dp[e.to][1] + dp[e.to][2]);
                    if((j & 1) == 0) tmp[j | 1] += dp[v][j] * dp[e.to][1];
                    if((j & 2) == 0) tmp[j | 2] += dp[v][j] * dp[e.to][1];
                }
                dp[v] = tmp;
            }
        }
    }

};


signed main(){

    int N; cin >> N;
    Graph G(N);
    REP(i, N - 1){
        int a, b; cin >> a >> b;
        G.add_Undirected_edge(a - 1, b - 1);
    }

    int v1, v2;
    int R = G.diameter(v1, v2);
    vec d1(N, 0), d2(N, 0);
    G.dfs_for_calcdist(v1, -1, -1, d1);
    G.dfs_for_calcdist(v2, -1, -1, d2);

    vec center;
    REP(i, N) if(d1[i] + d2[i] == R && llabs(d1[i] - d2[i]) <= 1) center.pb(i);
    
    fill(all(d1), 0);
    fill(all(d2), 0);
    mint ans;
    if(SZ(center) == 1){
        G.dfs_for_calcdist(center[0], -1, -1, d1);
        REP(i, N) if(d1[i] == R / 2) G.f[i] = true;

        G.dfs(center[0], -1);
        ans = G.dp[center[0]][3] / 2;
    }else{
        G.dfs_for_calcdist(center[0], -1, -1, d1);
        G.dfs_for_calcdist(center[1], -1, -1, d2);
        REP(i, N) if(min(d1[i], d2[i]) == R / 2) G.f[i] = true;

        G.dfs(center[0], center[1]);
        G.dfs(center[1], center[0]);
        ans = G.dp[center[0]][1] * G.dp[center[1]][1];
    }
    Out(ans);

    return 0;
}