human
A positive integer is called composite if it can be represented as a product of two positive integers, both greater than 1. For example, the following numbers are composite: 6, 4, 120, 27. The following numbers aren't: 1, 2, 3, 17, 97.

Alice is given a sequence of n composite numbers a_1,a_2,…,a_n.

She wants to choose an integer m ≤ 11 and color each element one of m colors from 1 to m so that:

  * for each color from 1 to m there is at least one element of this color.

  * each element is colored and colored exactly one color.

  * the greatest common divisor of any two elements that are colored the same color is greater than 1, i.e. \gcd(a_i, a_j)>1 for each pair i, j if these elements are colored the same color. 


Note that equal elements can be colored different colors — you just have to choose one of m colors for each of the indices from 1 to n.

Alice showed already that if all a_i ≤ 1000 then she can always solve the task by choosing some m ≤ 11.

Help Alice to find the required coloring. Note that you don't have to minimize or maximize the number of colors, you just have to find the solution with some m from 1 to 11.

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases. Then the descriptions of the test cases follow.

The first line of the test case contains a single integer n (1 ≤ n ≤ 1000) — the amount of numbers in a sequence a.

The second line of the test case contains n composite integers a_1,a_2,…,a_n (4 ≤ a_i ≤ 1000).

It is guaranteed that the sum of n over all test cases doesn't exceed 10^4.

Output

For each test case print 2 lines. The first line should contain a single integer m (1 ≤ m ≤ 11) — the number of used colors. Consider colors to be numbered from 1 to m. The second line should contain any coloring that satisfies the above conditions. Print n integers c_1, c_2, ..., c_n (1 ≤ c_i ≤ m), where c_i is the color of the i-th element. If there are multiple solutions then you can print any of them. Note that you don't have to minimize or...
from  Give me a Python code to find the required coloring?
assistant
#Here is Python code to find the required coloring.
__future__ import division, print_function
def main():
    def gcd(a,b):
        while b:
            a, b = b, a%b
        return a
    
    for _ in range(int(input())):
        n = int(input())
        
        l1 = list(map(int, input().split()))
        colored = [0] *n 
        primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
        used = {}
        color = 1
        for i in range(n):
            for p in primes:
                if l1[i]%p == 0:
                    if p in used:
                        colored[i] = used[p]
                    else:
                        colored[i] = color
                        used[p] = color
                        color +=1
                    break
        print(color-1)
        print(*colored)
        
        #for x in l1:
        #    print(colored[x],end = " ")
        #print("")
                    
######## Python 2 and 3 footer by Pajenegod and c1729

# Note because cf runs old PyPy3 version which doesn't have the sped up
# unicode strings, PyPy3 strings will many times be slower than pypy2.
# There is a way to get around this by using binary strings in PyPy3
# but its syntax is different which makes it kind of a mess to use.

# So on cf, use PyPy2 for best string performance.

py2 = round(0.5)
if py2:
    from future_builtins import ascii, filter, hex, map, oct, zip
    range = xrange

import os, sys
from io import IOBase, BytesIO

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:
    ...