Buggy python submission (verdict: Runtime Error):
def main():
    n = int(input())
    ab = [list(map(int, input().split())) for _ in [0]*(n-1)]

    g = [[] for _ in [0]*n]
    [g[a-1].append(b-1) for a, b in ab]
    [g[b-1].append(a-1) for a, b in ab]
    for root in range(n):
        if len(g[root]) > 2:
            break
    else:
        if n % 2:
            print("First")
        else:
            print("Second")
        return

    d = [-1]*n  # 根からの距離
    d[root] = 0
    q = [root]
    cnt = 0
    while q:  # BFS
        cnt += 1
        qq = []
        while q:
            i = q.pop()
            for j in g[i]:
                if d[j] == -1:
                    d[j] = cnt
                    qq.append(j)
        q = qq
    d2 = sorted([(j, i) for i, j in enumerate(d)])[::-1]
    end = [False]*n
    dp = [[] for _ in [0]*n]
    for _, i in d2:
        if len(g[i]) > 2:
            continue
        elif len(g[i]) == 1:
            dp[g[i][0]].append(1)
            if len(dp[g[i][0]]) > 1:
                end[g[i][0]] = True
        elif not end[i] and dp[i]:
            dist = dp[i][0]
            for j in g[i]:
                if d[j] < d[i]:
                    dp[j].append(dist+1)
    dp = [[j % 2 for j in i] for i in dp]
    one = set()
    for j, i in enumerate(dp):
        if i.count(1) > 1:
            print("First")
            return
        elif i.count(1) == 1:
            one.add(j)
    for i in one:
        q = [i]
        visited = {i}
        cnt = 1
        while q:
            qq = []
            j = q.pop()
            for k in g[j]:
                if k in visited:
                    continue
                visited.add(k)
                if len(g[k]) > 2:
                    if cnt % 2 == 0:
                        if k in one:
                            print(1/0)
                            print("First")
                            return
                elif len(g[k]) == 2:
                    qq.append(k)
            cnt += 1
            q = qq
    print("Second")


main()


Fixed submission:
def main():
    n = int(input())
    ab = [list(map(int, input().split())) for _ in [0]*(n-1)]
    g = [set() for _ in [0]*n]
    [g[a-1].add(b-1) for a, b in ab]
    [g[b-1].add(a-1) for a, b in ab]
    only = []
    sign = [False]*n
    for i in range(n):
        if len(g[i]) == 1:
            only.append(i)
    while only:
        i = only.pop()
        if not g[i]:
            print("Second")
            return
        j = g[i].pop()
        g[j].remove(i)
        if sign[i] and not g[j]:
            print("First")
            return
        if not sign[i] and sign[j]:
            print("First")
            return
        if not sign[j] and not sign[i]:
            sign[j] = True
        if len(g[j]) == 1:
            only.append(j)


main()

Buggy python submission (verdict: Runtime Error):
def main():
    n = int(input())
    ab = [list(map(int, input().split())) for _ in [0]*(n-1)]
    g = [[] for _ in [0]*n]
    [g[a-1].append(b-1) for a, b in ab]
    [g[b-1].append(a-1) for a, b in ab]
    for root in range(n):
        if len(g[root]) > 2:
            break
    else:
        if n % 2:
            print("First")
        else:
            print("Second")
        return

    d = [-1]*n  # 根からの距離
    d[root] = 0
    q = [root]
    cnt = 0
    while q:  # BFS
        cnt += 1
        qq = []
        while q:
            i = q.pop()
            for j in g[i]:
                if d[j] == -1:
                    d[j] = cnt
                    qq.append(j)
        q = qq
    d2 = sorted([(j, i) for i, j in enumerate(d)])[::-1]
    dp = [[] for _ in [0]*n]
    for _, i in d2:
        if len(g[i]) > 2:
            continue
        elif len(g[i]) == 1:
            dp[g[i][0]].append(1)
        else:
            dist = dp[i][0]
            for j in g[i]:
                if d[j] < d[i]:
                    dp[j].append(dist+1)
    dp = [[j % 2 for j in i] for i in dp]
    for i in dp:
        if i.count(1) > 1:
            print("First")
            return
    print("Second")


main()


Fixed submission:
def main():
    n = int(input())
    ab = [list(map(int, input().split())) for _ in [0]*(n-1)]
    g = [set() for _ in [0]*n]
    [g[a-1].add(b-1) for a, b in ab]
    [g[b-1].add(a-1) for a, b in ab]
    only = []
    sign = [False]*n
    for i in range(n):
        if len(g[i]) == 1:
            only.append(i)
    while only:
        i = only.pop()
        if not g[i]:
            print("Second")
            return
        j = g[i].pop()
        g[j].remove(i)
        if sign[i] and not g[j]:
            print("First")
            return
        if not sign[i] and sign[j]:
            print("First")
            return
        if not sign[j] and not sign[i]:
            sign[j] = True
        if len(g[j]) == 1:
            only.append(j)


main()

Buggy python submission (verdict: Runtime Error):
def main():
    n = int(input())
    ab = [list(map(int, input().split())) for _ in [0]*(n-1)]
    g = [[] for _ in [0]*n]
    [g[a-1].append(b-1) for a, b in ab]
    [g[b-1].append(a-1) for a, b in ab]
    for i in range(n):
        if len(g[i]) > 1:
            cnt = 0
            for j in g[i]:
                if len(g[j]) == 1:
                    cnt += 1
            if cnt > 1:
                print("First")
                return
    print(1/0)


main()

Fixed submission:
def main():
    n = int(input())
    ab = [list(map(int, input().split())) for _ in [0]*(n-1)]
    g = [set() for _ in [0]*n]
    [g[a-1].add(b-1) for a, b in ab]
    [g[b-1].add(a-1) for a, b in ab]
    only = []
    sign = [False]*n
    for i in range(n):
        if len(g[i]) == 1:
            only.append(i)
    while only:
        i = only.pop()
        if not g[i]:
            print("Second")
            return
        j = g[i].pop()
        g[j].remove(i)
        if sign[i] and not g[j]:
            print("First")
            return
        if not sign[i] and sign[j]:
            print("First")
            return
        if not sign[j] and not sign[i]:
            sign[j] = True
        if len(g[j]) == 1:
            only.append(j)


main()