Problem: A permutation is a sequence of n integers from 1 to n, in which all numbers occur exactly once. For example, [1], [3, 5, 2, 1, 4], [1, 3, 2] are permutations, and [2, 3, 2], [4, 3, 1], [0] are not.

Polycarp was presented with a permutation p of numbers from 1 to n. However, when Polycarp came home, he noticed that in his pocket, the permutation p had turned into an array q according to the following rule: 

  * q_i = max(p_1, p_2, …, p_i). 



Now Polycarp wondered what lexicographically minimal and lexicographically maximal permutations could be presented to him.

An array a of length n is lexicographically smaller than an array b of length n if there is an index i (1 ≤ i ≤ n) such that the first i-1 elements of arrays a and b are the same, and the i-th element of the array a is less than the i-th element of the array b. For example, the array a=[1, 3, 2, 3] is lexicographically smaller than the array b=[1, 3, 4, 2].

For example, if n=7 and p=[3, 2, 4, 1, 7, 5, 6], then q=[3, 3, 4, 4, 7, 7, 7] and the following permutations could have been as p initially: 

  * [3, 1, 4, 2, 7, 5, 6] (lexicographically minimal permutation); 
  * [3, 1, 4, 2, 7, 6, 5]; 
  * [3, 2, 4, 1, 7, 5, 6]; 
  * [3, 2, 4, 1, 7, 6, 5] (lexicographically maximum permutation). 



For a given array q, find the lexicographically minimal and lexicographically maximal permutations that could have been originally presented to Polycarp.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.

The first line of each test case contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5).

The second line of each test case contains n integers q_1, q_2, …, q_n (1 ≤ q_i ≤ n).

It is guaranteed that the array q was obtained by applying the rule from the statement to some permutation p.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output two lines: 

  * on the first line output n integers — lexicographically minimal permutation that could have been originally presented to Polycarp; 
  * on the second line print n integers — lexicographically maximal permutation that could have been originally presented to Polycarp; 

Example

Input


4
7
3 3 4 4 7 7 7
4
1 2 3 4
7
3 4 5 5 5 7 7
1
1


Output


3 1 4 2 7 5 6 
3 2 4 1 7 6 5 
1 2 3 4 
1 2 3 4 
3 4 5 1 2 7 6 
3 4 5 2 1 7 6 
1 
1 

Solution (in PYTHON3):

Solution:

from __future__ import print_function

import sys
import traceback

from bisect import bisect_left, bisect_right, insort
from itertools import chain, repeat, starmap
from math import log
from operator import add, eq, ne, gt, ge, lt, le, iadd
from textwrap import dedent


try:
    from collections.abc import Sequence, MutableSequence
except ImportError:
    from collections import Sequence, MutableSequence

from functools import wraps
from sys import hexversion

if hexversion < 0x03000000:
    from itertools import imap as map  
    from itertools import izip as zip  
    try:
        from thread import get_ident
    except ImportError:
        from dummy_thread import get_ident
else:
    from functools import reduce
    try:
        from _thread import get_ident
    except ImportError:
        from _dummy_thread import get_ident


def recursive_repr(fillvalue='...'):
    

    def decorating_function(user_function):
        repr_running = set()

        @wraps(user_function)
        def wrapper(self):
            key = id(self), get_ident()
            if key in repr_running:
                return fillvalue
            repr_running.add(key)
            try:
                result = user_function(self)
            finally:
                repr_running.discard(key)
            return result

        return wrapper

    return decorating_function



class SortedList(MutableSequence):
    DEFAULT_LOAD_FACTOR = 1000


    def __init__(self, iterable=None, key=None):
       
        assert key is None
        self._len = 0
        self._load = self.DEFAULT_LOAD_FACTOR
        self._lists = []
        self._maxes = []
        self._index = []
        self._offset = 0

        if iterable is not None:
            self._update(iterable)


    def __new__(cls, iterable=None, key=None):
        
        if key is None:
            return object.__new__(cls)
        else:
            if cls is SortedList:
                return object.__new__(SortedKeyList)
            else:
                raise TypeError('inherit SortedKeyList for key argument')


    @property
    def key(self):  
        
        return None


    def _reset(self, load):
        
        values = reduce(iadd, self._lists, [])
        self._clear()
        self._load = load
        self._update(values)


    def clear(self):
        
        self._len = 0
        del self._lists[:]
        del self._maxes[:]
        del self._index[:]
        self._offset = 0

    _clear = clear


    def add(self, value):
        
        _lists = self._lists
        _maxes = self._maxes

        if _maxes:
            pos = bisect_right(_maxes, value)

            if pos == len(_maxes):
                pos -= 1
                _lists[pos].append(value)
                _maxes[pos] = value
            else:
                insort(_lists[pos], value)

            self._expand(pos)
        else:
            _lists.append([value])
            _maxes.append(value)

        self._len += 1


    def _expand(self, pos):
       
        _load = self._load
        _lists = self._lists
        _index = self._index

        if len(_lists[pos]) > (_load << 1):
            _maxes = self._maxes

            _lists_pos = _lists[pos]
            half = _lists_pos[_load:]
            del _lists_pos[_load:]
            _maxes[pos] = _lists_pos[-1]

            _lists.insert(pos + 1, half)
            _maxes.insert(pos + 1, half[-1])

            del _index[:]
        else:
            if _index:
                child = self._offset + pos
                while child:
                    _index[child] += 1
                    child = (child - 1) >> 1
                _index[0] += 1


    def update(self, iterable):
  
        _lists = self._lists
        _maxes = self._maxes
        values = sorted(iterable)

        if _maxes:
            if len(values) * 4 >= self._len:
                values.extend(chain.from_iterable(_lists))
                values.sort()
                self._clear()
            else:
                _add = self.add
                for val in values:
                    _add(val)
                return

        _load = self._load
        _lists.extend(values[pos:(pos + _load)]
                      for pos in range(0, len(values), _load))
        _maxes.extend(sublist[-1] for sublist in _lists)
        self._len = len(values)
        del self._index[:]

    _update = update


    def __contains__(self, value):
       
        _maxes = self._maxes

        if not _maxes:
            return False

        pos = bisect_left(_maxes, value)

        if pos == len(_maxes):
            return False

        _lists = self._lists
        idx = bisect_left(_lists[pos], value)

        return _lists[pos][idx] == value


    def discard(self, value):
        
        _maxes = self._maxes

        if not _maxes:
            return

        pos = bisect_left(_maxes, value)

        if pos == len(_maxes):
            return

        _lists = self._lists
        idx = bisect_left(_lists[pos], value)

        if _lists[pos][idx] == value:
            self._delete(pos, idx)


    def remove(self, value):
        
        _maxes = self._maxes

        if not _maxes:
            raise ValueError('{0!r} not in list'.format(value))

        pos = bisect_left(_maxes, value)

        if pos == len(_maxes):
            raise ValueError('{0!r} not in list'.format(value))

        _lists = self._lists
        idx = bisect_left(_lists[pos], value)

        if _lists[pos][idx] == value:
            self._delete(pos, idx)
        else:
            raise ValueError('{0!r} not in list'.format(value))


    def _delete(self, pos, idx):
        
        _lists = self._lists
        _maxes = self._maxes
        _index = self._index

        _lists_pos = _lists[pos]

        del _lists_pos[idx]
        self._len -= 1

        len_lists_pos = len(_lists_pos)

        if len_lists_pos > (self._load >> 1):
            _maxes[pos] = _lists_pos[-1]

            if _index:
                child = self._offset + pos
                while child > 0:
                    _index[child] -= 1
                    child = (child - 1) >> 1
                _index[0] -= 1
        elif len(_lists) > 1:
            if not pos:
                pos += 1

            prev = pos - 1
            _lists[prev].extend(_lists[pos])
            _maxes[prev] = _lists[prev][-1]

            del _lists[pos]
            del _maxes[pos]
            del _index[:]

            self._expand(prev)
        elif len_lists_pos:
            _maxes[pos] = _lists_pos[-1]
        else:
            del _lists[pos]
            del _maxes[pos]
            del _index[:]


    def _loc(self, pos, idx):

        if not pos:
            return idx

        _index = self._index

        if not _index:
            self._build_index()

        total = 0

       

        pos += self._offset

        

        while pos:

            
            if not pos & 1:
                total += _index[pos - 1]

            pos = (pos - 1) >> 1

        return total + idx


    def _pos(self, idx):

        if idx < 0:
            last_len = len(self._lists[-1])

            if (-idx) <= last_len:
                return len(self._lists) - 1, last_len + idx

            idx += self._len

            if idx < 0:
                raise IndexError('list index out of range')
        elif idx >= self._len:
            raise IndexError('list index out of range')

        if idx < len(self._lists[0]):
            return 0, idx

        _index = self._index

        if not _index:
            self._build_index()

        pos = 0
        child = 1
        len_index = len(_index)

        while child < len_index:
            index_child = _index[child]

            if idx < index_child:
                pos = child
            else:
                idx -= index_child
                pos = child + 1

            child = (pos << 1) + 1

        return (pos - self._offset, idx)


    def _build_index(self):
      
        row0 = list(map(len, self._lists))

        if len(row0) == 1:
            self._index[:] = row0
            self._offset = 0
            return

        head = iter(row0)
        tail = iter(head)
        row1 = list(starmap(add, zip(head, tail)))

        if len(row0) & 1:
            row1.append(row0[-1])

        if len(row1) == 1:
            self._index[:] = row1 + row0
            self._offset = 1
            return

        size = 2 ** (int(log(len(row1) - 1, 2)) + 1)
        row1.extend(repeat(0, size - len(row1)))
        tree = [row0, row1]

        while len(tree[-1]) > 1:
            head = iter(tree[-1])
            tail = iter(head)
            row = list(starmap(add, zip(head, tail)))
            tree.append(row)

        reduce(iadd, reversed(tree), self._index)
        self._offset = size * 2 - 1


    def __delitem__(self, index):
        
        if isinstance(index, slice):
            start, stop, step = index.indices(self._len)

            if step == 1 and start < stop:
                if start == 0 and stop == self._len:
                    return self._clear()
                elif self._len <= 8 * (stop - start):
                    values = self._getitem(slice(None, start))
                    if stop < self._len:
                        values += self._getitem(slice(stop, None))
                    self._clear()
                    return self._update(values)

            indices = range(start, stop, step)


            if step > 0:
                indices = reversed(indices)

            _pos, _delete = self._pos, self._delete

            for index in indices:
                pos, idx = _pos(index)
                _delete(pos, idx)
        else:
            pos, idx = self._pos(index)
            self._delete(pos, idx)


    def __getitem__(self, index):
       
        _lists = self._lists

        if isinstance(index, slice):
            start, stop, step = index.indices(self._len)

            if step == 1 and start < stop:
               
                if start == 0 and stop == self._len:
                    return reduce(iadd, self._lists, [])

                start_pos, start_idx = self._pos(start)
                start_list = _lists[start_pos]
                stop_idx = start_idx + stop - start

                

                if len(start_list) >= stop_idx:
                    return start_list[start_idx:stop_idx]

                if stop == self._len:
                    stop_pos = len(_lists) - 1
                    stop_idx = len(_lists[stop_pos])
                else:
                    stop_pos, stop_idx = self._pos(stop)

                prefix = _lists[start_pos][start_idx:]
                middle = _lists[(start_pos + 1):stop_pos]
                result = reduce(iadd, middle, prefix)
                result += _lists[stop_pos][:stop_idx]

                return result

            if step == -1 and start > stop:
                result = self._getitem(slice(stop + 1, start + 1))
                result.reverse()
                return result

            

            indices = range(start, stop, step)
            return list(self._getitem(index) for index in indices)
        else:
            if self._len:
                if index == 0:
                    return _lists[0][0]
                elif index == -1:
                    return _lists[-1][-1]
            else:
                raise IndexError('list index out of range')

            if 0 <= index < len(_lists[0]):
                return _lists[0][index]

            len_last = len(_lists[-1])

            if -len_last < index < 0:
                return _lists[-1][len_last + index]

            pos, idx = self._pos(index)
            return _lists[pos][idx]

    _getitem = __getitem__


    def __setitem__(self, index, value):
        
        message = 'use ``del sl[index]`` and ``sl.add(value)`` instead'
        raise NotImplementedError(message)


    def __iter__(self):
        
        return chain.from_iterable(self._lists)


    def __reversed__(self):
       
        return chain.from_iterable(map(reversed, reversed(self._lists)))


    def reverse(self):
        
        raise NotImplementedError('use ``reversed(sl)`` instead')


    def islice(self, start=None, stop=None, reverse=False):
        
        _len = self._len

        if not _len:
            return iter(())

        start, stop, _ = slice(start, stop).indices(self._len)

        if start >= stop:
            return iter(())

        _pos = self._pos

        min_pos, min_idx = _pos(start)

        if stop == _len:
            max_pos = len(self._lists) - 1
            max_idx = len(self._lists[-1])
        else:
            max_pos, max_idx = _pos(stop)

        return self._islice(min_pos, min_idx, max_pos, max_idx, reverse)


    def _islice(self, min_pos, min_idx, max_pos, max_idx, reverse):
       
        _lists = self._lists

        if min_pos > max_pos:
            return iter(())

        if min_pos == max_pos:
            if reverse:
                indices = reversed(range(min_idx, max_idx))
                return map(_lists[min_pos].__getitem__, indices)

            indices = range(min_idx, max_idx)
            return map(_lists[min_pos].__getitem__, indices)

        next_pos = min_pos + 1

        if next_pos == max_pos:
            if reverse:
                min_indices = range(min_idx, len(_lists[min_pos]))
                max_indices = range(max_idx)
                return chain(
                    map(_lists[max_pos].__getitem__, reversed(max_indices)),
                    map(_lists[min_pos].__getitem__, reversed(min_indices)),
                )

            min_indices = range(min_idx, len(_lists[min_pos]))
            max_indices = range(max_idx)
            return chain(
                map(_lists[min_pos].__getitem__, min_indices),
                map(_lists[max_pos].__getitem__, max_indices),
            )

        if reverse:
            min_indices = range(min_idx, len(_lists[min_pos]))
            sublist_indices = range(next_pos, max_pos)
            sublists = map(_lists.__getitem__, reversed(sublist_indices))
            max_indices = range(max_idx)
            return chain(
                map(_lists[max_pos].__getitem__, reversed(max_indices)),
                chain.from_iterable(map(reversed, sublists)),
                map(_lists[min_pos].__getitem__, reversed(min_indices)),
            )

        min_indices = range(min_idx, len(_lists[min_pos]))
        sublist_indices = range(next_pos, max_pos)
        sublists = map(_lists.__getitem__, sublist_indices)
        max_indices = range(max_idx)
        return chain(
            map(_lists[min_pos].__getitem__, min_indices),
            chain.from_iterable(sublists),
            map(_lists[max_pos].__getitem__, max_indices),
        )


    def irange(self, minimum=None, maximum=None, inclusive=(True, True),
               reverse=False):
        
        _maxes = self._maxes

        if not _maxes:
            return iter(())

        _lists = self._lists


        if minimum is None:
            min_pos = 0
            min_idx = 0
        else:
            if inclusive[0]:
                min_pos = bisect_left(_maxes, minimum)

                if min_pos == len(_maxes):
                    return iter(())

                min_idx = bisect_left(_lists[min_pos], minimum)
            else:
                min_pos = bisect_right(_maxes, minimum)

                if min_pos == len(_maxes):
                    return iter(())

                min_idx = bisect_right(_lists[min_pos], minimum)


        if maximum is None:
            max_pos = len(_maxes) - 1
            max_idx = len(_lists[max_pos])
        else:
            if inclusive[1]:
                max_pos = bisect_right(_maxes, maximum)

                if max_pos == len(_maxes):
                    max_pos -= 1
                    max_idx = len(_lists[max_pos])
                else:
                    max_idx = bisect_right(_lists[max_pos], maximum)
            else:
                max_pos = bisect_left(_maxes, maximum)

                if max_pos == len(_maxes):
                    max_pos -= 1
                    max_idx = len(_lists[max_pos])
                else:
                    max_idx = bisect_left(_lists[max_pos], maximum)

        return self._islice(min_pos, min_idx, max_pos, max_idx, reverse)


    def __len__(self):
        
        return self._len


    def bisect_left(self, value):
        
        _maxes = self._maxes

        if not _maxes:
            return 0

        pos = bisect_left(_maxes, value)

        if pos == len(_maxes):
            return self._len

        idx = bisect_left(self._lists[pos], value)
        return self._loc(pos, idx)


    def bisect_right(self, value):
        
        _maxes = self._maxes

        if not _maxes:
            return 0

        pos = bisect_right(_maxes, value)

        if pos == len(_maxes):
            return self._len

        idx = bisect_right(self._lists[pos], value)
        return self._loc(pos, idx)

    bisect = bisect_right
    _bisect_right = bisect_right


    def count(self, value):
        
        _maxes = self._maxes

        if not _maxes:
            return 0

        pos_left = bisect_left(_maxes, value)

        if pos_left == len(_maxes):
            return 0

        _lists = self._lists
        idx_left = bisect_left(_lists[pos_left], value)
        pos_right = bisect_right(_maxes, value)

        if pos_right == len(_maxes):
            return self._len - self._loc(pos_left, idx_left)

        idx_right = bisect_right(_lists[pos_right], value)

        if pos_left == pos_right:
            return idx_right - idx_left

        right = self._loc(pos_right, idx_right)
        left = self._loc(pos_left, idx_left)
        return right - left


    def copy(self):
        
        return self.__class__(self)

    __copy__ = copy


    def append(self, value):
        
        raise NotImplementedError('use ``sl.add(value)`` instead')


    def extend(self, values):
        
        raise NotImplementedError('use ``sl.update(values)`` instead')


    def insert(self, index, value):
        
        raise NotImplementedError('use ``sl.add(value)`` instead')


    def pop(self, index=-1):
        
        if not self._len:
            raise IndexError('pop index out of range')

        _lists = self._lists

        if index == 0:
            val = _lists[0][0]
            self._delete(0, 0)
            return val

        if index == -1:
            pos = len(_lists) - 1
            loc = len(_lists[pos]) - 1
            val = _lists[pos][loc]
            self._delete(pos, loc)
            return val

        if 0 <= index < len(_lists[0]):
            val = _lists[0][index]
            self._delete(0, index)
            return val

        len_last = len(_lists[-1])

        if -len_last < index < 0:
            pos = len(_lists) - 1
            loc = len_last + index
            val = _lists[pos][loc]
            self._delete(pos, loc)
            return val

        pos, idx = self._pos(index)
        val = _lists[pos][idx]
        self._delete(pos, idx)
        return val


    def index(self, value, start=None, stop=None):
        
        _len = self._len

        if not _len:
            raise ValueError('{0!r} is not in list'.format(value))

        if start is None:
            start = 0
        if start < 0:
            start += _len
        if start < 0:
            start = 0

        if stop is None:
            stop = _len
        if stop < 0:
            stop += _len
        if stop > _len:
            stop = _len

        if stop <= start:
            raise ValueError('{0!r} is not in list'.format(value))

        _maxes = self._maxes
        pos_left = bisect_left(_maxes, value)

        if pos_left == len(_maxes):
            raise ValueError('{0!r} is not in list'.format(value))

        _lists = self._lists
        idx_left = bisect_left(_lists[pos_left], value)

        if _lists[pos_left][idx_left] != value:
            raise ValueError('{0!r} is not in list'.format(value))

        stop -= 1
        left = self._loc(pos_left, idx_left)

        if start <= left:
            if left <= stop:
                return left
        else:
            right = self._bisect_right(value) - 1

            if start <= right:
                return start

        raise ValueError('{0!r} is not in list'.format(value))


    def __add__(self, other):
        
        values = reduce(iadd, self._lists, [])
        values.extend(other)
        return self.__class__(values)

    __radd__ = __add__


    def __iadd__(self, other):
        
        self._update(other)
        return self


    def __mul__(self, num):
        
        values = reduce(iadd, self._lists, []) * num
        return self.__class__(values)

    __rmul__ = __mul__


    def __imul__(self, num):
        
        values = reduce(iadd, self._lists, []) * num
        self._clear()
        self._update(values)
        return self


    def __make_cmp(seq_op, symbol, doc):
        
        def comparer(self, other):
            
            if not isinstance(other, Sequence):
                return NotImplemented

            self_len = self._len
            len_other = len(other)

            if self_len != len_other:
                if seq_op is eq:
                    return False
                if seq_op is ne:
                    return True

            for alpha, beta in zip(self, other):
                if alpha != beta:
                    return seq_op(alpha, beta)

            return seq_op(self_len, len_other)

        seq_op_name = seq_op.__name__
        comparer.__name__ = '__{0}__'.format(seq_op_name)
        doc_str = """Return true if and only if sorted list is {0} `other`.

        ``sl.__{1}__(other)`` <==> ``sl {2} other``

        Comparisons use lexicographical order as with sequences.

        Runtime complexity: `O(n)`

        :param other: `other` sequence
        :return: true if sorted list is {0} `other`

        """
        comparer.__doc__ = dedent(doc_str.format(doc, seq_op_name, symbol))
        return comparer


    __eq__ = __make_cmp(eq, '==', 'equal to')
    __ne__ = __make_cmp(ne, '!=', 'not equal to')
    __lt__ = __make_cmp(lt, '<', 'less than')
    __gt__ = __make_cmp(gt, '>', 'greater than')
    __le__ = __make_cmp(le, '<=', 'less than or equal to')
    __ge__ = __make_cmp(ge, '>=', 'greater than or equal to')
    __make_cmp = staticmethod(__make_cmp)


    def __reduce__(self):
        values = reduce(iadd, self._lists, [])
        return (type(self), (values,))


    @recursive_repr()
    def __repr__(self):
        
        return '{0}({1!r})'.format(type(self).__name__, list(self))


    def _check(self):
        
        try:
            assert self._load >= 4
            assert len(self._maxes) == len(self._lists)
            assert self._len == sum(len(sublist) for sublist in self._lists)


            for sublist in self._lists:
                for pos in range(1, len(sublist)):
                    assert sublist[pos - 1] <= sublist[pos]


            for pos in range(1, len(self._lists)):
                assert self._lists[pos - 1][-1] <= self._lists[pos][0]


            for pos in range(len(self._maxes)):
                assert self._maxes[pos] == self._lists[pos][-1]

            double = self._load << 1
            assert all(len(sublist) <= double for sublist in self._lists)


            half = self._load >> 1
            for pos in range(0, len(self._lists) - 1):
                assert len(self._lists[pos]) >= half

            if self._index:
                assert self._len == self._index[0]
                assert len(self._index) == self._offset + len(self._lists)


                for pos in range(len(self._lists)):
                    leaf = self._index[self._offset + pos]
                    assert leaf == len(self._lists[pos])

                for pos in range(self._offset):
                    child = (pos << 1) + 1
                    if child >= len(self._index):
                        assert self._index[pos] == 0
                    elif child + 1 == len(self._index):
                        assert self._index[pos] == self._index[child]
                    else:
                        child_sum = self._index[child] + self._index[child + 1]
                        assert child_sum == self._index[pos]
        except:
            traceback.print_exc(file=sys.stdout)
            print('len', self._len)
            print('load', self._load)
            print('offset', self._offset)
            print('len_index', len(self._index))
            print('index', self._index)
            print('len_maxes', len(self._maxes))
            print('maxes', self._maxes)
            print('len_lists', len(self._lists))
            print('lists', self._lists)
            raise


def identity(value):
    
    return value


class SortedKeyList(SortedList):

    def __init__(self, iterable=None, key=identity):
        
        self._key = key
        self._len = 0
        self._load = self.DEFAULT_LOAD_FACTOR
        self._lists = []
        self._keys = []
        self._maxes = []
        self._index = []
        self._offset = 0

        if iterable is not None:
            self._update(iterable)


    def __new__(cls, iterable=None, key=identity):
        return object.__new__(cls)


    @property
    def key(self):
        
        return self._key


    def clear(self):
        
        self._len = 0
        del self._lists[:]
        del self._keys[:]
        del self._maxes[:]
        del self._index[:]

    _clear = clear


    def add(self, value):
        
        _lists = self._lists
        _keys = self._keys
        _maxes = self._maxes

        key = self._key(value)

        if _maxes:
            pos = bisect_right(_maxes, key)

            if pos == len(_maxes):
                pos -= 1
                _lists[pos].append(value)
                _keys[pos].append(key)
                _maxes[pos] = key
            else:
                idx = bisect_right(_keys[pos], key)
                _lists[pos].insert(idx, value)
                _keys[pos].insert(idx, key)

            self._expand(pos)
        else:
            _lists.append([value])
            _keys.append([key])
            _maxes.append(key)

        self._len += 1


    def _expand(self, pos):
        
        _lists = self._lists
        _keys = self._keys
        _index = self._index

        if len(_keys[pos]) > (self._load << 1):
            _maxes = self._maxes
            _load = self._load

            _lists_pos = _lists[pos]
            _keys_pos = _keys[pos]
            half = _lists_pos[_load:]
            half_keys = _keys_pos[_load:]
            del _lists_pos[_load:]
            del _keys_pos[_load:]
            _maxes[pos] = _keys_pos[-1]

            _lists.insert(pos + 1, half)
            _keys.insert(pos + 1, half_keys)
            _maxes.insert(pos + 1, half_keys[-1])

            del _index[:]
        else:
            if _index:
                child = self._offset + pos
                while child:
                    _index[child] += 1
                    child = (child - 1) >> 1
                _index[0] += 1


    def update(self, iterable):
        
        _lists = self._lists
        _keys = self._keys
        _maxes = self._maxes
        values = sorted(iterable, key=self._key)

        if _maxes:
            if len(values) * 4 >= self._len:
                values.extend(chain.from_iterable(_lists))
                values.sort(key=self._key)
                self._clear()
            else:
                _add = self.add
                for val in values:
                    _add(val)
                return

        _load = self._load
        _lists.extend(values[pos:(pos + _load)]
                      for pos in range(0, len(values), _load))
        _keys.extend(list(map(self._key, _list)) for _list in _lists)
        _maxes.extend(sublist[-1] for sublist in _keys)
        self._len = len(values)
        del self._index[:]

    _update = update


    def __contains__(self, value):
        
        _maxes = self._maxes

        if not _maxes:
            return False

        key = self._key(value)
        pos = bisect_left(_maxes, key)

        if pos == len(_maxes):
            return False

        _lists = self._lists
        _keys = self._keys

        idx = bisect_left(_keys[pos], key)

        len_keys = len(_keys)
        len_sublist = len(_keys[pos])

        while True:
            if _keys[pos][idx] != key:
                return False
            if _lists[pos][idx] == value:
                return True
            idx += 1
            if idx == len_sublist:
                pos += 1
                if pos == len_keys:
                    return False
                len_sublist = len(_keys[pos])
                idx = 0


    def discard(self, value):
        
        _maxes = self._maxes

        if not _maxes:
            return

        key = self._key(value)
        pos = bisect_left(_maxes, key)

        if pos == len(_maxes):
            return

        _lists = self._lists
        _keys = self._keys
        idx = bisect_left(_keys[pos], key)
        len_keys = len(_keys)
        len_sublist = len(_keys[pos])

        while True:
            if _keys[pos][idx] != key:
                return
            if _lists[pos][idx] == value:
                self._delete(pos, idx)
                return
            idx += 1
            if idx == len_sublist:
                pos += 1
                if pos == len_keys:
                    return
                len_sublist = len(_keys[pos])
                idx = 0


    def remove(self, value):
        
        _maxes = self._maxes

        if not _maxes:
            raise ValueError('{0!r} not in list'.format(value))

        key = self._key(value)
        pos = bisect_left(_maxes, key)

        if pos == len(_maxes):
            raise ValueError('{0!r} not in list'.format(value))

        _lists = self._lists
        _keys = self._keys
        idx = bisect_left(_keys[pos], key)
        len_keys = len(_keys)
        len_sublist = len(_keys[pos])

        while True:
            if _keys[pos][idx] != key:
                raise ValueError('{0!r} not in list'.format(value))
            if _lists[pos][idx] == value:
                self._delete(pos, idx)
                return
            idx += 1
            if idx == len_sublist:
                pos += 1
                if pos == len_keys:
                    raise ValueError('{0!r} not in list'.format(value))
                len_sublist = len(_keys[pos])
                idx = 0


    def _delete(self, pos, idx):
        
        _lists = self._lists
        _keys = self._keys
        _maxes = self._maxes
        _index = self._index
        keys_pos = _keys[pos]
        lists_pos = _lists[pos]

        del keys_pos[idx]
        del lists_pos[idx]
        self._len -= 1

        len_keys_pos = len(keys_pos)

        if len_keys_pos > (self._load >> 1):
            _maxes[pos] = keys_pos[-1]

            if _index:
                child = self._offset + pos
                while child > 0:
                    _index[child] -= 1
                    child = (child - 1) >> 1
                _index[0] -= 1
        elif len(_keys) > 1:
            if not pos:
                pos += 1

            prev = pos - 1
            _keys[prev].extend(_keys[pos])
            _lists[prev].extend(_lists[pos])
            _maxes[prev] = _keys[prev][-1]

            del _lists[pos]
            del _keys[pos]
            del _maxes[pos]
            del _index[:]

            self._expand(prev)
        elif len_keys_pos:
            _maxes[pos] = keys_pos[-1]
        else:
            del _lists[pos]
            del _keys[pos]
            del _maxes[pos]
            del _index[:]


    def irange(self, minimum=None, maximum=None, inclusive=(True, True),
               reverse=False):
        
        min_key = self._key(minimum) if minimum is not None else None
        max_key = self._key(maximum) if maximum is not None else None
        return self._irange_key(
            min_key=min_key, max_key=max_key,
            inclusive=inclusive, reverse=reverse,
        )


    def irange_key(self, min_key=None, max_key=None, inclusive=(True, True),
                   reverse=False):
        
        _maxes = self._maxes

        if not _maxes:
            return iter(())

        _keys = self._keys

        if min_key is None:
            min_pos = 0
            min_idx = 0
        else:
            if inclusive[0]:
                min_pos = bisect_left(_maxes, min_key)

                if min_pos == len(_maxes):
                    return iter(())

                min_idx = bisect_left(_keys[min_pos], min_key)
            else:
                min_pos = bisect_right(_maxes, min_key)

                if min_pos == len(_maxes):
                    return iter(())

                min_idx = bisect_right(_keys[min_pos], min_key)

        if max_key is None:
            max_pos = len(_maxes) - 1
            max_idx = len(_keys[max_pos])
        else:
            if inclusive[1]:
                max_pos = bisect_right(_maxes, max_key)

                if max_pos == len(_maxes):
                    max_pos -= 1
                    max_idx = len(_keys[max_pos])
                else:
                    max_idx = bisect_right(_keys[max_pos], max_key)
            else:
                max_pos = bisect_left(_maxes, max_key)

                if max_pos == len(_maxes):
                    max_pos -= 1
                    max_idx = len(_keys[max_pos])
                else:
                    max_idx = bisect_left(_keys[max_pos], max_key)

        return self._islice(min_pos, min_idx, max_pos, max_idx, reverse)

    _irange_key = irange_key


    def bisect_left(self, value):
        
        return self._bisect_key_left(self._key(value))


    def bisect_right(self, value):
        
        return self._bisect_key_right(self._key(value))

    bisect = bisect_right


    def bisect_key_left(self, key):
        
        _maxes = self._maxes

        if not _maxes:
            return 0

        pos = bisect_left(_maxes, key)

        if pos == len(_maxes):
            return self._len

        idx = bisect_left(self._keys[pos], key)

        return self._loc(pos, idx)

    _bisect_key_left = bisect_key_left


    def bisect_key_right(self, key):
        
        _maxes = self._maxes

        if not _maxes:
            return 0

        pos = bisect_right(_maxes, key)

        if pos == len(_maxes):
            return self._len

        idx = bisect_right(self._keys[pos], key)

        return self._loc(pos, idx)

    bisect_key = bisect_key_right
    _bisect_key_right = bisect_key_right


    def count(self, value):
        
        _maxes = self._maxes

        if not _maxes:
            return 0

        key = self._key(value)
        pos = bisect_left(_maxes, key)

        if pos == len(_maxes):
            return 0

        _lists = self._lists
        _keys = self._keys
        idx = bisect_left(_keys[pos], key)
        total = 0
        len_keys = len(_keys)
        len_sublist = len(_keys[pos])

        while True:
            if _keys[pos][idx] != key:
                return total
            if _lists[pos][idx] == value:
                total += 1
            idx += 1
            if idx == len_sublist:
                pos += 1
                if pos == len_keys:
                    return total
                len_sublist = len(_keys[pos])
                idx = 0


    def copy(self):
        
        return self.__class__(self, key=self._key)

    __copy__ = copy


    def index(self, value, start=None, stop=None):
        
        _len = self._len

        if not _len:
            raise ValueError('{0!r} is not in list'.format(value))

        if start is None:
            start = 0
        if start < 0:
            start += _len
        if start < 0:
            start = 0

        if stop is None:
            stop = _len
        if stop < 0:
            stop += _len
        if stop > _len:
            stop = _len

        if stop <= start:
            raise ValueError('{0!r} is not in list'.format(value))

        _maxes = self._maxes
        key = self._key(value)
        pos = bisect_left(_maxes, key)

        if pos == len(_maxes):
            raise ValueError('{0!r} is not in list'.format(value))

        stop -= 1
        _lists = self._lists
        _keys = self._keys
        idx = bisect_left(_keys[pos], key)
        len_keys = len(_keys)
        len_sublist = len(_keys[pos])

        while True:
            if _keys[pos][idx] != key:
                raise ValueError('{0!r} is not in list'.format(value))
            if _lists[pos][idx] == value:
                loc = self._loc(pos, idx)
                if start <= loc <= stop:
                    return loc
                elif loc > stop:
                    break
            idx += 1
            if idx == len_sublist:
                pos += 1
                if pos == len_keys:
                    raise ValueError('{0!r} is not in list'.format(value))
                len_sublist = len(_keys[pos])
                idx = 0

        raise ValueError('{0!r} is not in list'.format(value))


    def __add__(self, other):
        
        values = reduce(iadd, self._lists, [])
        values.extend(other)
        return self.__class__(values, key=self._key)

    __radd__ = __add__


    def __mul__(self, num):
        
        values = reduce(iadd, self._lists, []) * num
        return self.__class__(values, key=self._key)


    def __reduce__(self):
        values = reduce(iadd, self._lists, [])
        return (type(self), (values, self.key))


    @recursive_repr()
    def __repr__(self):
        
        type_name = type(self).__name__
        return '{0}({1!r}, key={2!r})'.format(type_name, list(self), self._key)


    def _check(self):
        
        try:
            assert self._load >= 4
            assert len(self._maxes) == len(self._lists) == len(self._keys)
            assert self._len == sum(len(sublist) for sublist in self._lists)

            for sublist in self._keys:
                for pos in range(1, len(sublist)):
                    assert sublist[pos - 1] <= sublist[pos]

            for pos in range(1, len(self._keys)):
                assert self._keys[pos - 1][-1] <= self._keys[pos][0]

            for val_sublist, key_sublist in zip(self._lists, self._keys):
                assert len(val_sublist) == len(key_sublist)
                for val, key in zip(val_sublist, key_sublist):
                    assert self._key(val) == key


            for pos in range(len(self._maxes)):
                assert self._maxes[pos] == self._keys[pos][-1]

            double = self._load << 1
            assert all(len(sublist) <= double for sublist in self._lists)


            half = self._load >> 1
            for pos in range(0, len(self._lists) - 1):
                assert len(self._lists[pos]) >= half

            if self._index:
                assert self._len == self._index[0]
                assert len(self._index) == self._offset + len(self._lists)

                for pos in range(len(self._lists)):
                    leaf = self._index[self._offset + pos]
                    assert leaf == len(self._lists[pos])

                for pos in range(self._offset):
                    child = (pos << 1) + 1
                    if child >= len(self._index):
                        assert self._index[pos] == 0
                    elif child + 1 == len(self._index):
                        assert self._index[pos] == self._index[child]
                    else:
                        child_sum = self._index[child] + self._index[child + 1]
                        assert child_sum == self._index[pos]
        except:
            traceback.print_exc(file=sys.stdout)
            print('len', self._len)
            print('load', self._load)
            print('offset', self._offset)
            print('len_index', len(self._index))
            print('index', self._index)
            print('len_maxes', len(self._maxes))
            print('maxes', self._maxes)
            print('len_keys', len(self._keys))
            print('keys', self._keys)
            print('len_lists', len(self._lists))
            print('lists', self._lists)
            raise


SortedListWithKey = SortedKeyList


from bisect import *
from collections import *
from math import gcd,ceil,sqrt,floor,inf
from heapq import *
from itertools import *
from operator import add,mul,sub,xor,truediv,floordiv
from functools import *
 
#------------------------------------------------------------------------
import os
import sys

from io import BytesIO, IOBase
# region fastio
 
BUFSIZE = 8192
 
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
 
 
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
 
 
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
 

#------------------------------------------------------------------------
def RL(): return map(int, sys.stdin.readline().rstrip().split())
def RLL(): return list(map(int, sys.stdin.readline().rstrip().split()))
def N(): return int(input())
def A(n):return [0]*n
def AI(n,x): return [x]*n
def G(n): return [[] for i in range(n)]
def GP(it): return [[ch,len(list(g))] for ch,g in groupby(it)]
#------------------------------------------------------------------------


from types import GeneratorType
 
 
def bootstrap(f, stack=[]):
    def wrappedfunc(*args, **kwargs):
        if stack:
            return f(*args, **kwargs)
        else:
            to = f(*args, **kwargs)
            while True:
                if type(to) is GeneratorType:
                    stack.append(to)
                    to = next(to)
                else:
                    stack.pop()
                    if not stack:
                        break
                    to = stack[-1].send(to)
            return to
 
    return wrappedfunc
 
 
farr=[1]
ifa=[]
 
def fact(x,mod=0):
    if mod:
        while x>=len(farr):
            farr.append(farr[-1]*len(farr)%mod)
    else:
        while x>=len(farr):
            farr.append(farr[-1]*len(farr))
    return farr[x]
 
def ifact(x,mod):
    global ifa
    ifa.append(pow(farr[-1],mod-2,mod))
    for i in range(x,0,-1):
        ifa.append(ifa[-1]*i%mod)
    ifa=ifa[::-1]
 
def per(i,j,mod=0):
    if i<j: return 0
    if not mod:
        return fact(i)//fact(i-j)
    return farr[i]*ifa[i-j]%mod
    
def com(i,j,mod=0):
    if i<j: return 0
    if not mod:        
        return per(i,j)//fact(j)
    return per(i,j,mod)*ifa[j]%mod
 
def catalan(n):
    return com(2*n,n)//(n+1)
 
def isprime(n):
    for i in range(2,int(n**0.5)+1):
        if n%i==0:
            return False
    return True
 
def lowbit(n):
    return n&-n
 
def inverse(a,m):
    a%=m
    if a<=1: return a
    return ((1-inverse(m,a)*m)//a)%m
 
class BIT:
    def __init__(self,arr):
        self.arr=arr
        self.n=len(arr)-1
        
    def update(self,x,v):
        while x<=self.n:
            self.arr[x]+=v
            x+=x&-x
 
    def query(self,x):
        ans=0
        while x:
            ans+=self.arr[x]
            x&=x-1
        return ans
'''
class SMT:
    def __init__(self,arr):
        self.n=len(arr)-1
        self.arr=[0]*(self.n<<2)
        self.lazy=[0]*(self.n<<2)
        def Build(l,r,rt):
            if l==r:
                self.arr[rt]=arr[l]
                return
            m=(l+r)>>1
            Build(l,m,rt<<1)
            Build(m+1,r,rt<<1|1)
            self.pushup(rt)
        Build(1,self.n,1)
 
    def pushup(self,rt):
        self.arr[rt]=self.arr[rt<<1]+self.arr[rt<<1|1]
 
    def pushdown(self,rt,ln,rn):#lr,rn表区间数字数
        if self.lazy[rt]:
            self.lazy[rt<<1]+=self.lazy[rt]
            self.lazy[rt<<1|1]+=self.lazy[rt]
            self.arr[rt<<1]+=self.lazy[rt]*ln
            self.arr[rt<<1|1]+=self.lazy[rt]*rn
            self.lazy[rt]=0
            
    def update(self,L,R,c,l=1,r=None,rt=1):#L,R表示操作区间
        if r==None: r=self.n
        if L<=l and r<=R:
            self.arr[rt]+=c*(r-l+1)
            self.lazy[rt]+=c
            return
        m=(l+r)>>1
        self.pushdown(rt,m-l+1,r-m)
        if L<=m: self.update(L,R,c,l,m,rt<<1)
        if R>m: self.update(L,R,c,m+1,r,rt<<1|1)
        self.pushup(rt)
 
    def query(self,L,R,l=1,r=None,rt=1):
        if r==None: r=self.n
        #print(L,R,l,r,rt)
        if L<=l and R>=r:
            return self.arr[rt]
        m=(l+r)>>1
        self.pushdown(rt,m-l+1,r-m)
        ans=0
        if L<=m: ans+=self.query(L,R,l,m,rt<<1)
        if R>m: ans+=self.query(L,R,m+1,r,rt<<1|1)
        return ans
'''       
class DSU:#容量+路径压缩
    def __init__(self,n):
        self.c=[-1]*n
 
    def same(self,x,y):
        return self.find(x)==self.find(y)
 
    def find(self,x):
        if self.c[x]<0:
            return x
        self.c[x]=self.find(self.c[x])
        return self.c[x]
 
    def union(self,u,v):
        u,v=self.find(u),self.find(v)
        if u==v:
            return False
        if self.c[u]<self.c[v]:
            u,v=v,u
        self.c[u]+=self.c[v]
        self.c[v]=u
        return True
 
    def size(self,x): return -self.c[self.find(x)]
    
class UFS:#秩+路径
    def __init__(self,n):
        self.parent=[i for i in range(n)]
        self.ranks=[0]*n
 
    def find(self,x):
        if x!=self.parent[x]:
            self.parent[x]=self.find(self.parent[x])
        return self.parent[x]
 
    def union(self,u,v):
        pu,pv=self.find(u),self.find(v)
        if pu==pv:
            return False
        if self.ranks[pu]>=self.ranks[pv]:
            self.parent[pv]=pu
            if self.ranks[pv]==self.ranks[pu]:
                self.ranks[pu]+=1
        else:
            self.parent[pu]=pv
 
def Prime(n):
    c=0
    prime=[]
    flag=[0]*(n+1)
    
    for i in range(2,n+1):
        if not flag[i]:
            prime.append(i)
            c+=1
        for j in range(c):
            if i*prime[j]>n: break
            flag[i*prime[j]]=prime[j]
            if i%prime[j]==0: break
    #print(flag)
    return flag,prime
 
def dij(s,graph):
    d={}
    d[s]=0
    heap=[(0,s)]
    seen=set()
    while heap:
        dis,u=heappop(heap)
        if u in seen:
            continue
        for v in graph[u]:
            if v not in d or d[v]>d[u]+graph[u][v]:
                d[v]=d[u]+graph[u][v]
                heappush(heap,(d[v],v))
    return d
 
def GP(it): return [[ch,len(list(g))] for ch,g in groupby(it)]
 
class DLN:
    def __init__(self,val):
        self.val=val
        self.pre=None
        self.next=None

def nb(i,j):
    for ni,nj in [[i+1,j],[i-1,j],[i,j-1],[i,j+1]]:
        if 0<=ni<n and 0<=nj<m:
            yield ni,nj
            
@bootstrap
def gdfs(r,p):
    if len(g[r])==1 and p!=-1:
        yield None
    for ch in g[r]:
        if ch!=p:
            yield gdfs(ch,r)
    yield None




t=N()
for i in range(t):
    n=N()
    q=RLL()
    vis=A(n+1)
    mi=A(n)
    ma=A(n)
    mi[0]=ma[0]=q[0]
    vis[q[0]]=1
    for i in range(1,n):
        if q[i]>q[i-1]:
            vis[q[i]]=1
            mi[i]=ma[i]=q[i]
    res=[]
    for i in range(1,n+1):
        if not vis[i]:
            res.append(i)
    s1=sorted(res)
    s2=SortedList(res)
    j=0
    last=0
    for i in range(n):
        if mi[i]==0:
            mi[i]=s1[j]
            ind=s2.bisect(last)
            ma[i]=s2[ind-1]
            s2.remove(ma[i])
            j+=1
        else:last=mi[i]
    print(*mi)
    print(*ma)
   # print(ans)

''' 
sys.setrecursionlimit(200000)
import threading
threading.stack_size(10**8)
t=threading.Thread(target=main)
t.start()
t.join()
'''

''' 
sys.setrecursionlimit(200000)
import threading
threading.stack_size(10**8)
t=threading.Thread(target=main)
t.start()
t.join()
'''