Buggy python submission (verdict: Runtime Error):
import sys
input = sys.stdin.readline
mod=998244353

N=int(input())
E=[[] for i in range(N+1)]

for i in range(N-1):
    x,y=map(int,input().split())
    E[x].append(y)
    E[y].append(x)

Q=[1]
D=[-1]*(N+1)
D[1]=0
while Q:
    x=Q.pop()
    for to in E[x]:
        if D[to]==-1:
            D[to]=D[x]+1
            Q.append(to)
            
f=D.index(max(D))
Q=[f]
D=[-1]*(N+1)
D[f]=0
while Q:
    x=Q.pop()
    for to in E[x]:
        if D[to]==-1:
            D[to]=D[x]+1
            Q.append(to)

MAX=max(D)
l=D.index(MAX)
Q=[l]
D2=[-1]*(N+1)
D2[l]=0
while Q:
    x=Q.pop()
    for to in E[x]:
        if D2[to]==-1:
            D2[to]=D2[x]+1
            Q.append(to)

if MAX%2==0:
    for i in range(N+1):
        if D[i]==MAX//2 and D2[i]==MAX//2:
            c=i
            break
        
    TOP_SORT=[]
    
    Q=[c]
    D=[-1]*(N+1)
    P=[-1]*(N+1)
    D[c]=0
    while Q:
        x=Q.pop()
        TOP_SORT.append(x)
        for to in E[x]:
            if D[to]==-1:
                D[to]=D[x]+1
                Q.append(to)
                P[to]=x

    DP=[[[0,0,0] for i in range(3)] for i in range(N+1)]
    # DP[x][p][m]で, plusのものが0個, 1個, 2個以上, minusのものが0個, 1個, 2個以上

    for x in TOP_SORT[::-1]:
        if D[x]==MAX//2:
            DP[x][1][1]=1

        elif len(E[x])==1:
            DP[x][0][0]=1
            
        else:
            for to in E[x]:
                if to==P[x]:
                    continue

                X=[[0,0,0] for i in range(3)]
                for i in range(3):
                    for j in range(3):
                        X[0][0]+=DP[to][i][j]
                        X[i][0]+=DP[to][i][j]
                        X[0][j]+=DP[to][i][j]
                
                if DP[x]==[[0,0,0] for i in range(3)]:
                    DP[x]=X
                    
                else:
                    Y=[[0,0,0] for i in range(3)]

                    for i in range(3):
                        for j in range(3):
                            for k in range(3):
                                for l in range(3):
                                    Y[min(2,i+k)][min(2,j+l)]=(Y[min(2,i+k)][min(2,j+l)]+X[i][j]*DP[x][k][l])%mod

                    DP[x]=Y

    #print(DP)
    print(DP[c][1][1]*pow(2,mod-2,mod)%mod)
    
else:
    A[10000]
            
            
                    
                
                
            

        

            
            



Fixed submission:
import sys
input = sys.stdin.readline
mod=998244353

N=int(input())
E=[[] for i in range(N+1)]

for i in range(N-1):
    x,y=map(int,input().split())
    E[x].append(y)
    E[y].append(x)

Q=[1]
D=[-1]*(N+1)
D[1]=0
while Q:
    x=Q.pop()
    for to in E[x]:
        if D[to]==-1:
            D[to]=D[x]+1
            Q.append(to)
            
f=D.index(max(D))
Q=[f]
D=[-1]*(N+1)
D[f]=0
while Q:
    x=Q.pop()
    for to in E[x]:
        if D[to]==-1:
            D[to]=D[x]+1
            Q.append(to)

MAX=max(D)
l=D.index(MAX)
Q=[l]
D2=[-1]*(N+1)
D2[l]=0
while Q:
    x=Q.pop()
    for to in E[x]:
        if D2[to]==-1:
            D2[to]=D2[x]+1
            Q.append(to)

if MAX%2==0:
    for i in range(N+1):
        if D[i]==MAX//2 and D2[i]==MAX//2:
            c=i
            break
        
    TOP_SORT=[]
    
    Q=[c]
    D=[-1]*(N+1)
    P=[-1]*(N+1)
    D[c]=0
    while Q:
        x=Q.pop()
        TOP_SORT.append(x)
        for to in E[x]:
            if D[to]==-1:
                D[to]=D[x]+1
                Q.append(to)
                P[to]=x

    DP=[[[0,0,0] for i in range(3)] for i in range(N+1)]
    # DP[x][p][m]で, plusのものが0個, 1個, 2個以上, minusのものが0個, 1個, 2個以上

    for x in TOP_SORT[::-1]:
        if D[x]==MAX//2:
            DP[x][1][1]=1

        elif len(E[x])==1:
            DP[x][0][0]=1
            
        else:
            for to in E[x]:
                if to==P[x]:
                    continue

                X=[[0,0,0] for i in range(3)]
                for i in range(3):
                    for j in range(3):
                        X[0][0]+=DP[to][i][j]
                        X[i][0]+=DP[to][i][j]
                        X[0][j]+=DP[to][i][j]
                
                if DP[x]==[[0,0,0] for i in range(3)]:
                    DP[x]=X
                    
                else:
                    Y=[[0,0,0] for i in range(3)]

                    for i in range(3):
                        for j in range(3):
                            for k in range(3):
                                for l in range(3):
                                    Y[min(2,i+k)][min(2,j+l)]=(Y[min(2,i+k)][min(2,j+l)]+X[i][j]*DP[x][k][l])%mod

                    DP[x]=Y

    #print(DP)
    print(DP[c][1][1]*pow(2,mod-2,mod)%mod)
    
else:
    for i in range(N+1):
        if D[i]==MAX//2 and D2[i]==MAX//2+1:
            c1=i
        elif D[i]==MAX//2+1 and D2[i]==MAX//2:
            c2=i
        
    TOP_SORT=[]
    
    Q=[c1,c2]
    D=[-1]*(N+1)
    P=[-1]*(N+1)
    D[c1]=0
    D[c2]=0
    P[c1]=c2
    P[c2]=c1
    
    while Q:
        x=Q.pop()
        TOP_SORT.append(x)
        for to in E[x]:
            if D[to]==-1:
                D[to]=D[x]+1
                Q.append(to)
                P[to]=x

    DP=[[[0,0,0] for i in range(3)] for i in range(N+1)]
    # DP[x][p][m]で, plusのものが0個, 1個, 2個以上, minusのものが0個, 1個, 2個以上

    for x in TOP_SORT[::-1]:
        if D[x]==MAX//2:
            DP[x][1][1]=1

        elif len(E[x])==1:
            DP[x][0][0]=1
            
        else:
            for to in E[x]:
                if to==P[x]:
                    continue

                X=[[0,0,0] for i in range(3)]
                for i in range(3):
                    for j in range(3):
                        X[0][0]+=DP[to][i][j]
                        X[i][0]+=DP[to][i][j]
                        X[0][j]+=DP[to][i][j]
                
                if DP[x]==[[0,0,0] for i in range(3)]:
                    DP[x]=X
                    
                else:
                    Y=[[0,0,0] for i in range(3)]

                    for i in range(3):
                        for j in range(3):
                            for k in range(3):
                                for l in range(3):
                                    Y[min(2,i+k)][min(2,j+l)]=(Y[min(2,i+k)][min(2,j+l)]+X[i][j]*DP[x][k][l])%mod

                    DP[x]=Y

    #print(DP[c1])
    #print(DP[c2])
    print(sum(DP[c1][1])*sum(DP[c2][1])%mod)

Buggy python submission (verdict: Runtime Error):
import sys
input = sys.stdin.readline
mod=998244353

N=int(input())
E=[[] for i in range(N+1)]

for i in range(N-1):
    x,y=map(int,input().split())
    E[x].append(y)
    E[y].append(x)

Q=[1]
D=[-1]*(N+1)
D[1]=0
while Q:
    x=Q.pop()
    for to in E[x]:
        if D[to]==-1:
            D[to]=D[x]+1
            Q.append(to)
            
f=D.index(max(D))
Q=[f]
D=[-1]*(N+1)
D[f]=0
while Q:
    x=Q.pop()
    for to in E[x]:
        if D[to]==-1:
            D[to]=D[x]+1
            Q.append(to)

MAX=max(D)
l=D.index(MAX)
Q=[l]
D2=[-1]*(N+1)
D2[l]=0
while Q:
    x=Q.pop()
    for to in E[x]:
        if D2[to]==-1:
            D2[to]=D2[x]+1
            Q.append(to)

if MAX%2==0:
    for i in range(N+1):
        if D[i]==MAX//2 and D2[i]==MAX//2:
            c=i
            break
        
    TOP_SORT=[]
    
    Q=[c]
    D=[-1]*(N+1)
    P=[-1]*(N+1)
    D[c]=0
    while Q:
        x=Q.pop()
        TOP_SORT.append(x)
        for to in E[x]:
            if D[to]==-1:
                D[to]=D[x]+1
                Q.append(to)
                P[to]=x

    DP=[[0,0,0] for i in range(N+1)]
    # 中心からの距離が条件を満たすものが、0個, 1個, 2個以上

    for x in TOP_SORT[::-1]:
        if D[x]==MAX//2:
            DP[x]=[0,1,0]

        elif len(E[x])==1:
            DP[x]=[1,0,0]

        elif x==c:
            True
            
        else:
            for to in E[x]:
                if to==P[x]:
                    continue
                xt,yt,zt=DP[to]
                x1,y1,z1=xt*3+yt*2+zt*2,yt,zt
                
                if DP[x]==[0,0,0]:
                    DP[x]=[x1,y1,z1]
                else:
                    x0,y0,z0=DP[x]
                    DP[x]=[x0*x1%mod,(x1*y0+x0*y1)%mod,(y0*y1+z0*(x1+y1+z1)+z1*(x0+y0))%mod]

    ANS=[0,0,0] # 0個, 1個, 2個ちょうど
    for to in E[c]:
        xt,yt,zt=DP[to]
        x1,y1,z1=xt*3+yt*2+zt*2,yt,zt
        
        if ANS==[0,0,0]:
            ANS=[x1,y1,z1]

        else:
            x0,y0,z0=ANS
            ANS=[x0*x1%mod,(x1*y0+x0*y1)%mod,(y1*y0+y0*y1)%mod]

    print(ANS[2]*pow(2,mod-2,mod)%mod)
else:
    A[10000]

Fixed submission:
import sys
input = sys.stdin.readline
mod=998244353

N=int(input())
E=[[] for i in range(N+1)]

for i in range(N-1):
    x,y=map(int,input().split())
    E[x].append(y)
    E[y].append(x)

Q=[1]
D=[-1]*(N+1)
D[1]=0
while Q:
    x=Q.pop()
    for to in E[x]:
        if D[to]==-1:
            D[to]=D[x]+1
            Q.append(to)
            
f=D.index(max(D))
Q=[f]
D=[-1]*(N+1)
D[f]=0
while Q:
    x=Q.pop()
    for to in E[x]:
        if D[to]==-1:
            D[to]=D[x]+1
            Q.append(to)

MAX=max(D)
l=D.index(MAX)
Q=[l]
D2=[-1]*(N+1)
D2[l]=0
while Q:
    x=Q.pop()
    for to in E[x]:
        if D2[to]==-1:
            D2[to]=D2[x]+1
            Q.append(to)

if MAX%2==0:
    for i in range(N+1):
        if D[i]==MAX//2 and D2[i]==MAX//2:
            c=i
            break
        
    TOP_SORT=[]
    
    Q=[c]
    D=[-1]*(N+1)
    P=[-1]*(N+1)
    D[c]=0
    while Q:
        x=Q.pop()
        TOP_SORT.append(x)
        for to in E[x]:
            if D[to]==-1:
                D[to]=D[x]+1
                Q.append(to)
                P[to]=x

    DP=[[[0,0,0] for i in range(3)] for i in range(N+1)]
    # DP[x][p][m]で, plusのものが0個, 1個, 2個以上, minusのものが0個, 1個, 2個以上

    for x in TOP_SORT[::-1]:
        if D[x]==MAX//2:
            DP[x][1][1]=1

        elif len(E[x])==1:
            DP[x][0][0]=1
            
        else:
            for to in E[x]:
                if to==P[x]:
                    continue

                X=[[0,0,0] for i in range(3)]
                for i in range(3):
                    for j in range(3):
                        X[0][0]+=DP[to][i][j]
                        X[i][0]+=DP[to][i][j]
                        X[0][j]+=DP[to][i][j]
                
                if DP[x]==[[0,0,0] for i in range(3)]:
                    DP[x]=X
                    
                else:
                    Y=[[0,0,0] for i in range(3)]

                    for i in range(3):
                        for j in range(3):
                            for k in range(3):
                                for l in range(3):
                                    Y[min(2,i+k)][min(2,j+l)]=(Y[min(2,i+k)][min(2,j+l)]+X[i][j]*DP[x][k][l])%mod

                    DP[x]=Y

    #print(DP)
    print(DP[c][1][1]*pow(2,mod-2,mod)%mod)
    
else:
    for i in range(N+1):
        if D[i]==MAX//2 and D2[i]==MAX//2+1:
            c1=i
        elif D[i]==MAX//2+1 and D2[i]==MAX//2:
            c2=i
        
    TOP_SORT=[]
    
    Q=[c1,c2]
    D=[-1]*(N+1)
    P=[-1]*(N+1)
    D[c1]=0
    D[c2]=0
    P[c1]=c2
    P[c2]=c1
    
    while Q:
        x=Q.pop()
        TOP_SORT.append(x)
        for to in E[x]:
            if D[to]==-1:
                D[to]=D[x]+1
                Q.append(to)
                P[to]=x

    DP=[[[0,0,0] for i in range(3)] for i in range(N+1)]
    # DP[x][p][m]で, plusのものが0個, 1個, 2個以上, minusのものが0個, 1個, 2個以上

    for x in TOP_SORT[::-1]:
        if D[x]==MAX//2:
            DP[x][1][1]=1

        elif len(E[x])==1:
            DP[x][0][0]=1
            
        else:
            for to in E[x]:
                if to==P[x]:
                    continue

                X=[[0,0,0] for i in range(3)]
                for i in range(3):
                    for j in range(3):
                        X[0][0]+=DP[to][i][j]
                        X[i][0]+=DP[to][i][j]
                        X[0][j]+=DP[to][i][j]
                
                if DP[x]==[[0,0,0] for i in range(3)]:
                    DP[x]=X
                    
                else:
                    Y=[[0,0,0] for i in range(3)]

                    for i in range(3):
                        for j in range(3):
                            for k in range(3):
                                for l in range(3):
                                    Y[min(2,i+k)][min(2,j+l)]=(Y[min(2,i+k)][min(2,j+l)]+X[i][j]*DP[x][k][l])%mod

                    DP[x]=Y

    #print(DP[c1])
    #print(DP[c2])
    print(sum(DP[c1][1])*sum(DP[c2][1])%mod)