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.*;
import static java.lang.Math.*;
public class Main {
    static final long MOD = 1_000_000_007, INF = 1_000_000_000_000_000_000L;
    static final int INf = 1_000_000_000;
    static FastReader reader;
    static PrintWriter writer;
    public static void main(String[] args) {
        Thread t = new Thread(null, new O(), "Integer.MAX_VALUE", 100000000);
        t.start();
    }
    static class O implements Runnable {
        public void run() {
            try {
                magic();
            }
            catch (Exception e) {
                e.printStackTrace();
                System.exit(1);
            }
        }
    }
    static class FastReader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public FastReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public FastReader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64];
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (c == '.') while ((c = read()) >= '0' && c <= '9') ret += (c - '0') / (div *= 10);
            if (neg) return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null) return;
            din.close();
        }
    }
    //variables here
    static int BIT[][] = new int[200001][2];
    static int MAX = 200000;
    static void magic() throws IOException{
        reader = new FastReader();
        writer = new PrintWriter(System.out, true);
        StringBuilder fast = new StringBuilder();
        int t = reader.nextInt();
        while(t-->0) {
            int n = reader.nextInt();
            int l[] = new int[n], r[] = new int[n];
            int div = -1;
            for(int i=0;i<n;++i) {
                l[i] = reader.nextInt();
                r[i] = reader.nextInt();
                update(0,l[i],1);
                update(1, r[i], 1);
            }
            for(int i=0;i<n;++i) {
                int point = l[i];
                int idhar = query(1, point-1);
                int udhar = query(0, MAX) - query(0, point-1);
                if(idhar>0 && udhar>0 && idhar + udhar==n) {
                    div = point;
                }
            }
            if(div==-1) {
                fast.append("-1\n");
            }
            else {
                for(int i=0;i<n;++i) {
                   if(l[i]>=div) {
                       fast.append("1 ");
                   }
                   else {
                       fast.append("2 ");
                   }
                }
                fast.append("\n");
            }
            for(int i=0;i<n;++i) {
                update(0,l[i],-1);
                update(1, r[i], -1);
            }
        }
        writer.print(fast);
        writer.flush();
    }
    static void update(int id,int index,int val)
    {
        for(int i=index;i<=MAX;i+=i&-i)
            BIT[i][id]+=val;
    }
    static int query(int id, int index)
    {
        int sum = 0;
        for(int i=index;i>0;i-=i&-i)
            sum+=BIT[i][id];
        return sum;
    }
}