Problem: There are n segments [l_i, r_i] for 1 ≤ i ≤ n. You should divide all segments into two non-empty groups in such way that there is no pair of segments from different groups which have at least one common point, or say that it's impossible to do it. Each segment should belong to exactly one group.

To optimize testing process you will be given multitest.

Input

The first line contains one integer T (1 ≤ T ≤ 50000) — the number of queries. Each query contains description of the set of segments. Queries are independent.

First line of each query contains single integer n (2 ≤ n ≤ 10^5) — number of segments. It is guaranteed that ∑{n} over all queries does not exceed 10^5.

The next n lines contains two integers l_i, r_i per line (1 ≤ l_i ≤ r_i ≤ 2 ⋅ 10^5) — the i-th segment.

Output

For each query print n integers t_1, t_2, ..., t_n (t_i ∈ \{1, 2\}) — for each segment (in the same order as in the input) t_i equals 1 if the i-th segment will belongs to the first group and 2 otherwise.

If there are multiple answers, you can print any of them. If there is no answer, print -1.

Example

Input


3
2
5 5
2 3
3
3 5
2 3
2 3
3
3 3
4 4
5 5


Output


2 1 
-1
1 1 2 

Note

In the first query the first and the second segments should be in different groups, but exact numbers don't matter.

In the second query the third segment intersects with the first and the second segments, so they should be in the same group, but then the other group becomes empty, so answer is -1.

In the third query we can distribute segments in any way that makes groups non-empty, so any answer of 6 possible is correct.

Solution (in PYTHON3):

Solution:
from bisect import insort,bisect_right,bisect_left
from sys import stdout, stdin, setrecursionlimit
from heapq import heappush, heappop, heapify 
from io import BytesIO, IOBase
from collections import *
from itertools import *
from random import * 
from string import *
from queue import *
from math import *
from re import *
from os import *

# sqrt,ceil,floor,factorial,gcd,log2,log10,comb

####################################---fast-input-output----#########################################


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 = read(self._fd, max(fstat(self._fd).st_size, 8192))
            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 = read(self._fd, max(fstat(self._fd).st_size, 8192))
            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:
            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")


stdin, stdout = IOWrapper(stdin), IOWrapper(stdout)
graph, mod, szzz =  {}, 10**9 + 7, lambda: sorted(zzz())
def getStr(): return input()
def getInt(): return int(input())
def listStr(): return list(input())
def getStrs(): return input().split()
def isInt(s): return '0' <= s[0] <= '9'
def input(): return stdin.readline().strip()
def zzz(): return [int(i) for i in input().split()]
def output(answer, end='\n'): stdout.write(str(answer) + end)
def lcd(xnum1, xnum2): return (xnum1 * xnum2 // gcd(xnum1, xnum2))


def getPrimes(N = 10**5):
    SN = int(sqrt(N))
    sieve = [i for i in range(N+1)]
    sieve[1] = 0
    for i in sieve:
        if i > SN:
            break
        if i == 0:
            continue
        for j in range(2*i, N+1, i):
            sieve[j] = 0
    prime = [i for i in range(N+1) if sieve[i] != 0] 
    return prime
def primeFactor(n,prime=getPrimes()):
    lst = []
    mx=int(sqrt(n))+1
    for i in prime:
        if i>mx:break
        while n%i==0:
            lst.append(i)
            n//=i
    if n>1:
        lst.append(n)
    return lst    

dx = [-1, 1, 0, 0, 1, -1, 1, -1]
dy = [0, 0, 1, -1, 1, -1, -1, 1]
daysInMounth = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]


#################################################---Some Rule For Me To Follow---#################################
"""
    --instants of Reading problem continuously try to understand them.

    --Try & again try, maybe you're just one statement away!


"""
##################################################---START-CODING---###############################################


num = getInt()


for _ in range(num):

    n = getInt()
    points=[]
    for i in range(n):
        points.append((zzz(),i))

    points.sort()

    left = points[0][0][0]
    right = points[0][0][1]

    ok = 1
    ans = [0]*n
    for i in range(n):
        if points[i][0][0]>right:
            ok=2
        ans[points[i][1]]=ok
        right=max(right,points[i][0][1])

    print(*ans if ok-1 else [-1])