Problem: The round carousel consists of n figures of animals. Figures are numbered from 1 to n in order of the carousel moving. Thus, after the n-th figure the figure with the number 1 follows. Each figure has its own type — the type of the animal corresponding to this figure (the horse, the tiger and so on). The type of animal of the i-th figure equals t_i.

<image> The example of the carousel for n=9 and t=[5, 5, 1, 15, 1, 5, 5, 1, 1]. 

You want to color each figure in one of the colors. You think that it's boring if the carousel contains two different figures (with the distinct types of animals) going one right after another and colored in the same color.

Your task is to color the figures in such a way that the number of distinct colors used is the minimum possible and there are no figures of the different types going one right after another and colored in the same color. If you use exactly k distinct colors, then the colors of figures should be denoted with integers from 1 to k.

Input

The input contains one or more test cases.

The first line contains one integer q (1 ≤ q ≤ 10^4) — the number of test cases in the test. Then q test cases follow. One test case is given on two lines.

The first line of the test case contains one integer n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of figures in the carousel. Figures are numbered from 1 to n in order of carousel moving. Assume that after the n-th figure the figure 1 goes.

The second line of the test case contains n integers t_1, t_2, ..., t_n (1 ≤ t_i ≤ 2 ⋅ 10^5), where t_i is the type of the animal of the i-th figure.

The sum of n over all test cases does not exceed 2⋅10^5.

Output

Print q answers, for each test case print two lines.

In the first line print one integer k — the minimum possible number of distinct colors of figures.

In the second line print n integers c_1, c_2, ..., c_n (1 ≤ c_i ≤ k), where c_i is the color of the i-th figure. If there are several answers, you can print any.

Example

Input


4
5
1 2 1 2 2
6
1 2 2 1 2 2
5
1 2 1 2 3
3
10 10 10


Output


2
1 2 1 2 2
2
2 1 2 1 2 1
3
2 3 2 3 1
1
1 1 1 

Solution (in PYTHON3):

Solution:
import sys
import os
from io import IOBase, BytesIO
# import heapq
import math
# import collections
# import itertools
# import bisect
mod = 10 ** 9 + 7
pie = 3.1415926536
# import resource
# resource.setrlimit(resource.RLIMIT_STACK, [0x100000000, resource.RLIM_INFINITY])
# import threading
# threading.stack_size(2**27)
# import sys
# sys.setrecursionlimit(10**6)
# fact=[1]
# for i in range(1,1000001):
#    fact.append((fact[-1]*i)%mod)
# ifact=[0]*1000001
# ifact[1000000]=pow(fact[1000000],mod-2,mod)
# for i in range(1000000,0,-1):
#    ifact[i-1]=(i*ifact[i])%mod
# from random import randint as rn
# from Queue import Queue as Q


def modinv(n, p):
    return pow(n, p-2, p)


def ncr(n, r, p):  # for using this uncomment the lines calculating fact and ifact
    t = ((fact[n])*((ifact[r]*ifact[n-r]) % p)) % p
    return t


def ain():  # takes array as input
    return list(map(int, sin().split()))


def sin():
    return input().strip()


def GCD(x, y):
    while(y):
        x, y = y, x % y
    return x


def read2DIntArray(row, col):
    arr = []
    for i in range(0, row):
        temp = list(map(int, sin().split()))
        arr.append(temp)

    return arr


def read2DCharArray(row, col):
    arr = []
    for i in range(0, row):
        temp = str(sin())
        arr.append(temp)

    return arr


"""****************** SMALLEST NO. BY REARRANGING DIGITS OF n (WITHOUT TRAILING ZEROS) *********************"""


def smallestNumber(n):
    lst = list(str(n))
    lst.sort()

    tmp = ""
    for i, n in enumerate(lst):
        if (n != '0'):
            tmp = lst.pop(i)
            break

    return str(tmp) + ''.join(lst)


"""*********************** GENERATE ALL PRIME NUMBERS SMALLER THAN OR EQUAL TO n ***************************"""


def SieveOfEratosthenes(n):

    prime = [True for i in range(n + 1)]
    p = 2
    while (p * p <= n):

        if (prime[p] == True):
            for i in range(p * 2, n + 1, p):
                prime[i] = False

        p += 1
    prime[0] = False
    prime[1] = False

    lst = []
    for p in range(n + 1):
        if prime[p]:
            lst.append(p)

    return lst


"""*************************************** FIND nCr ********************************************************"""


def nCr(n, r):
    a = 1
    b = 1
    c = 1
    for i in range(1, n + 1):
        c *= i
    for i in range(1, r + 1):
        b *= i
    for i in range(1, n - r + 1):
        a *= i

    return (c // (a * b))


"""************************* GET PRIME FACTORS AND THEIR POWERS FOR AN INTEGER *****************************"""


def sieveOfEratosthenes1(N, s):

    prime = [False] * (N+1)

    for i in range(2, N+1, 2):
        s[i] = 2

    for i in range(3, N+1, 2):
        if (prime[i] == False):

            s[i] = i

            for j in range(i, int(N / i) + 1, 2):
                if (prime[i*j] == False):
                    prime[i*j] = True

                    s[i * j] = i


def generatePrimeFactors(N):

    s = [0] * (N+1)

    sieveOfEratosthenes1(N, s)

    # print("Factor Power")

    curr = s[N]

    cnt = 1

    factors = []
    power = []
    while (N > 1):
        N //= s[N]

        if (curr == s[N]):
            cnt += 1
            continue

        # curr is factor and cnt in the power of this factor
        factors.append(curr)
        power.append(cnt)

        curr = s[N]
        cnt = 1

    return factors, power


"""----------------------------------------------MAIN------------------------------------------------------"""


def main():
    for _ in range(int(sin())):
        n = int(sin())
        t = ain()

        flag = 0
        for i in range(n):
            if i > 0 and t[i] == t[i - 1]:
                flag = 1
                break

        tmp = set(t)

        res = []
        if len(tmp) == 1:
            res = [1] * n
        elif n % 2 == 0:
            for i in range(n):
                res.append((i % 2) + 1)
        elif flag == 0:
            for i in range(n - 1):
                res.append((i % 2) + 1)
            if t[0] != t[-1]:
                res.append(3)
            else:
                res.append(((n - 1) % 2) + 1)
        elif flag == 1:
            f = 0
            for i in range(n):
                if i > 0 and t[i] == t[i - 1] and f == 0:
                    res.append(((i - 1) % 2) + 1)
                    f = 1
                elif i > 0:
                    if res[i - 1] == 1:
                        res.append(2)
                    else:
                        res.append(1)
                else:
                    res.append((i % 2) + 1)

        print(max(res))
        print(*res)


"""--------------------------------------------------------------------------------------------------------"""

# Python 2 and 3 footer by Pajenegod and j1729
py2 = round(0.5)
if py2:
    from future_builtins import ascii, filter, hex, map, oct, zip
    range = xrange


BUFSIZE = 8192


class FastIO(BytesIO):
    newlines = 0

    def __init__(self, file):
        self._file = file
        self._fd = file.fileno()
        self.writable = "x" in file.mode or "w" in file.mode
        self.write = super(FastIO, self).write if self.writable else None

    def _fill(self):
        s = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
        self.seek((self.tell(), self.seek(0, 2),
                   super(FastIO, self).write(s))[0])
        return s

    def read(self):
        while self._fill():
            pass
        return super(FastIO, self).read()

    def readline(self):
        while self.newlines == 0:
            s = self._fill()
            self.newlines = s.count(b"\n") + (not s)
        self.newlines -= 1
        return super(FastIO, self).readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.getvalue())
            self.truncate(0), self.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        if py2:
            self.write = self.buffer.write
            self.read = self.buffer.read
            self.readline = self.buffer.readline
        else:
            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)


def input(): return sys.stdin.readline().rstrip('\r\n')


if __name__ == '__main__':
    main()
# threading.Thread(target=main).start()