Buggy python submission (verdict: Runtime Error):
from itertools import permutations
from heapq import *
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]

# smallで作った数列のチェック
def check_s(res, ngi):
    if res[0] == ngi: return False
    for i in range(len(res) - 1):
        if res[i + 1] == ng[res[i]]:
            return False
    return True

# nが小さいときの全探索用
def small(remain, ngi):
    for res in permutations(remain):
        if check_s(res, ngi): return res
    return [-2]

# 使った数を消しながら最小の数を返す
def delpop():
    while 1:
        i = heappop(hp)
        if not used[i]: return i

# 次の数を選ぶ
def next_i(ngi, cr):
    i = delpop()
    if i == ngi:
        ii = delpop()
        heappush(hp, i)
        i = ii
    ngj = ng[i]
    if used[ngj]: return i
    if indeg[ngj] < cr - 1: return i
    heappush(hp, i)
    return ngj

def main():
    # 頂点iを追加しても、残りの頂点でハミルトンパスが存在するかチェックしながら
    # 残りが4点になるまで小さい順に頂点を選んでいく
    ans = []
    ngi = -1
    cnt_remain = n
    for _ in range(n - 4):
        i = next_i(ngi, cnt_remain)
        ans.append(i)
        used[i] = True
        cnt_remain -= 1
        ngi = ng[i]
        indeg[ngi] -= 1
    # 4点以下の残りについては愚直に探す
    remain = []
    while hp: remain.append(delpop())
    ans += small(remain, ngi)
    ans = [x + 1 for x in ans]
    print(*ans)

n = II()
ng = LI1()
hp = list(range(n))
heapify(hp)
used = [False] * n
indeg = [0] * n
for k in ng: indeg[k] += 1
main()


Fixed submission:
from itertools import permutations
from heapq import *
import sys

sys.setrecursionlimit(10 ** 6)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]

# smallで作った数列のチェック
def check_s(res, ngi):
    if res[0] == ngi: return False
    for i in range(len(res) - 1):
        if res[i + 1] == ng[res[i]]:
            return False
    return True

# nが小さいときの全探索用
def small(remain, ngi):
    for res in permutations(remain):
        if check_s(res, ngi): return res
    return [-2]

# 使った数を消しながら最小の数を返す
def delpop():
    while 1:
        i = heappop(hp)
        if not used[i]: return i

# 次の数を選ぶ
def next_i(ngi, cr):
    i = delpop()
    if i == ngi:
        ii = delpop()
        heappush(hp, i)
        i = ii
    ngj = ng[i]
    if used[ngj]: return i
    if indeg[ngj] < cr - 1: return i
    heappush(hp, i)
    return ngj

def main():
    # 頂点iを追加しても、残りの頂点でハミルトンパスが存在するかチェックしながら
    # 残りが4点になるまで小さい順に頂点を選んでいく
    ans = []
    ngi = -1
    cnt_remain = n
    for _ in range(n - 4):
        i = next_i(ngi, cnt_remain)
        ans.append(i)
        used[i] = True
        cnt_remain -= 1
        ngi = ng[i]
        indeg[ngi] -= 1
    # 4点以下の残りについては愚直に探す
    remain = []
    while hp:
        i=heappop(hp)
        if used[i]:continue
        remain.append(i)
    ans += small(remain, ngi)
    ans = [x + 1 for x in ans]
    print(*ans)

n = II()
ng = LI1()
hp = list(range(n))
heapify(hp)
used = [False] * n
indeg = [0] * n
for k in ng: indeg[k] += 1
main()