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 JAVA):

Solution:
import java.util.*;
import java.io.*;



public class Main {
    static OutputWriter out;
    public static void main(String[] args)
    {
        InputReader in = new InputReader(System.in);
        out = new OutputWriter(System.out);
       int t = in.nextInt();
       while (t>0)
       {
           int n = in.nextInt();
           int[]l = new int[n];
           int[]r= new int[n];
           int[]index = new int[n];
           int ans = -1;
           for (int i =0;i<n;i++)
           {
               l[i]=in.nextInt();
               r[i]= in.nextInt();
               index[i] =i;
           }
           MergeSort(l,r,index,0,n-1);
           int max=r[0];
           int[]cntr= new int[n];
           int o=1;
           cntr[index[0]]=1;
           for (int i=1;i<n;i++)
           {
               if (l[i]>max)
               {
                       ans=i;
                       o=2;
               }
               cntr[index[i]]=o;
               max=Math.max(max,r[i]);
           }
           if (ans==-1)
               out.printLine(ans);
           else
           {
               for (int item:cntr
                    ) {
                   out.print(item+" ");
               }
               out.printLine();
           }
           t--;
       }
        out.flush();
    }
    static void MergeSort(int[] a, int[] b,int[]c,  int p, int r)
    {
        if (p < r)
        {
            int q = (r + p) / 2;
            MergeSort(a, b,c,  p, q);
            MergeSort(a, b,  c,q + 1, r);
            Merge(a, b, c,p, q, r);
        }
    }
    static void Merge(int[] a, int[] b,int[]c,int p, int q, int r)
    {
        int n1 = q - p + 1;
        int n2 = r - q;
        int[] R = new int[n1 + 1];
        int[] L = new int[n2 + 1];
        int[] R1 = new int[n1];
        int[] L1 = new int[n2];
        int[] R2 = new int[n1];
        int[] L2 = new int[n2];
        for (int i = 0; i < n1; i++)
        {
            R[i] = a[p + i];
            R1[i] = b[p + i];
            R2[i] = c[p + i];

        }
        R[n1] = Integer.MAX_VALUE;
        for (int i = 0; i < n2; i++)
        {
            L[i] = a[q + i + 1];
            L1[i] = b[q + i + 1];
            L2[i] = c[q + i + 1];

        }
        L[n2] =Integer.MAX_VALUE;
        int n = a.length;
        int j = 0;
        int k = 0;
        for (int i = p; i <= r; i++)
        {
            if (L[j] < R[k])
            {
                a[i] = L[j];
                b[i] = L1[j];
                c[i] = L2[j];

                j++;
            }
            else if (L[j]>R[k])
            {
                a[i] = R[k];
                b[i] = R1[k];
                c[i] = R2[k];
                k++;
            }
            else
            {
                if (L1[j] < R1[k])
                {
                    a[i] = L[j];
                    b[i] = L1[j];
                    c[i] = L2[j];
                    j++;
                }
                else
                {
                    a[i] = R[k];
                    b[i] = R1[k];
                    c[i] = R2[k];
                    k++;
                }
            }

        }
    }
}
class MyScanner {

    StringTokenizer st;
    BufferedReader br;

    public MyScanner(InputStream s) {
        br = new BufferedReader(new InputStreamReader(s));
    }

    public MyScanner (FileReader f) {
        br = new BufferedReader(f);
    }

    public String next() throws IOException {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    public int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    public long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    public String nextLine() throws IOException {
        return br.readLine();
    }

    public double nextDouble() throws IOException {
        String x = next();
        StringBuilder sb = new StringBuilder("0");
        double res = 0, f = 1;
        boolean dec = false, neg = false;
        int start = 0;
        if (x.charAt(0) == '-') {
            neg = true;
            start++;
        }
        for (int i = start; i < x.length(); i++)
            if (x.charAt(i) == '.') {
                res = Long.parseLong(sb.toString());
                sb = new StringBuilder("0");
                dec = true;
            } else {
                sb.append(x.charAt(i));
                if (dec)
                    f *= 10;
            }
        res += Long.parseLong(sb.toString()) / f;
        return res * (neg ? -1 : 1);
    }

    public boolean ready() throws IOException {
        return br.ready();
    }

    public boolean nextEmpty() throws IOException {
        String s = nextLine();
        st = new StringTokenizer(s);
        return s.isEmpty();
    }
}


class pair  implements Comparable
{
    int dist;
    int to;
    public pair(int to, int dist)
    {
        this.dist = dist;
        this.to = to;
    }
    @Override
    public int compareTo(Object o) {
        pair temp =(pair)o;
        if (dist<temp.dist)
            return -1;
        else if (dist>temp.dist)
            return 1;
        else
            return 0;
    }
}
class Graph {


    int n;
    ArrayList<pair>[] adjList;

    public Graph(int n) {
        this.n = n;
        adjList = new ArrayList[n];
        for (int i = 0; i < n; i++)
            adjList[i] = new ArrayList<>();
    }

}



class InputReader {

    private final InputStream stream;
    private final byte[] buf = new byte[8192];
    private int curChar, snumChars;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        if (snumChars == -1)
            throw new InputMismatchException();
        if (curChar >= snumChars) {
            curChar = 0;
            try {
                snumChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (snumChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int nextInt() {
        int c = read();
        while (isSpaceChar(c)) {
            c = read();
        }
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public long nextLong() {
        int c = read();
        while (isSpaceChar(c)) {
            c = read();
        }
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public int[] nextIntArray(int n) {
        int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    public String readString() {
        int c = read();
        while (isSpaceChar(c)) {
            c = read();
        }
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public String nextLine() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isEndOfLine(c));
        return res.toString();
    }

    public boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private boolean isEndOfLine(int c) {
        return c == '\n' || c == '\r' || c == -1;
    }

}

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }


    public void printLine(Object... objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }

    public void flush() {
        writer.flush();
    }

}