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:
    //    A Computer is Like a mischievous genie.
    //    It will give you exactly what you ask for,
    //    but not always what you want
    //    A code by Rahul Verma


    import java.io.BufferedOutputStream;
    import java.io.BufferedReader;
    import java.io.IOException;
    import java.io.InputStreamReader;
    import java.io.PrintWriter;
    import java.math.BigInteger;
    import java.util.ArrayList;
    import java.util.Arrays;
    import java.util.Collections;
    import java.util.Comparator;
    import java.util.HashMap;
    import java.util.HashSet;
    import java.util.LinkedHashSet;
    import java.util.LinkedList;
    import java.util.List;
    import java.util.PriorityQueue;
    import java.util.Queue;
    import java.util.Set;
    import java.util.Stack;
    import java.util.StringTokenizer;
    import java.util.TreeMap;
    import java.util.TreeSet;


    public class Main {


        static class Clock {

            protected long start, stop;

            public void start() {

                start = System.currentTimeMillis();
            }

            public void stop() {
                stop = System.currentTimeMillis();
            }

            public String getTime() {

                return ((stop - start) + " ms");
            }
        }


        public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

        static class FastReader {

            BufferedReader br;
            StringTokenizer st;

            public FastReader() {
                br = new BufferedReader(new
                    InputStreamReader(System.in));
            }

            String next() {
                while (st == null || !st.hasMoreElements()) {
                    try {
                        st = new StringTokenizer(br.readLine());
                    } catch (IOException e) {
                        e.printStackTrace();
                    }
                }
                return st.nextToken();
            }

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

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

            double nextDouble() {
                return Double.parseDouble(next());
            }

            String[] nextSArray() {
                String sr[] = null;
                try {
                    sr = br.readLine().trim().split(" ");
                } catch (IOException e) {
                    e.printStackTrace();
                }
                return sr;
            }

            String nextLine() {
                String str = "";
                try {
                    str = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }

                return str;
            }
        }


        static long powmodulo(long a, long p) {
            if (p == 0) {
                return 1 % mod;
            }
            if (p == 1) {
                return a % mod;
            }
            long ans = 1;
            while (p > 0) {
                if ((p & 1) > 0) {
                    ans = (ans * a) % mod;
                }
                a = (a * a) % mod;
                p = p >> 1;
            }
            return ans % mod;
        }


        static long mod = 1000000007;

        static long gcd(long a, long b) {
            if (a == 0) {
                return b;
            }
            return gcd(b % a, a);
        }

        static long fast_powerNumbers(long a, long n) {
            if (n == 1) {
                return a;
            }
            long ans = fast_powerNumbers(a, n / 2);
            if (n % 2 == 0) {
                return (ans * ans);
            } else {
                return ((ans * ans) * (a));
            }
        }


        static void dfs_helper(int[][] arr, int i, int j, int team, int n, int m) {
            arr[i][j] = team;
            if (i - 1 >= 0 && arr[i - 1][j] == 1) {
                dfs(arr, i - 1, j, team, n, m);
            }
            if (j - 1 >= 0 && arr[i][j - 1] == 1) {
                dfs(arr, i, j - 1, team, n, m);
            }
            if (i + 1 < n && arr[i + 1][j] == 1) {
                dfs(arr, i + 1, j, team, n, m);
            }
            if (j + 1 < m && arr[i][j + 1] == 1) {
                dfs(arr, i, j + 1, team, n, m);
            }

        }

        static void dfs(int[][] arr, int i, int j, int team, int n, int m) {
            dfs_helper(arr, i, j, team, n, m);

        }
        public static int arr[];


        static void seive(int n) {
            // 1 is not prime
            arr = new int[n + 1];
            arr[0] = arr[1] = 1;
            for (int i = 4; i <= n; i = i + 2) {
                arr[i] = 1;
            }
            for (int i = 3; i * i <= n; i = i + 2) {
                if (arr[i] == 0) {
                    for (int j = i * i; j <= n; j = j + i) {
                        arr[j] = 1;
                    }

                }
            }
        }


        public static HashMap<Integer,Integer> primefac(int n)
        {
            HashMap<Integer,Integer>hm=new HashMap<>();
            //int x = (int) Math.sqrt(n);
            for (int i = 2; i <=n; i++) {
                int x=0;
                while(n%i==0)
                {
                    n=n/i;
                    ++x;
                }
                if(x!=0)
                {
                    hm.put(i,x);
                }
            }
            return hm;
        }
       static long fac(int p)
       {
           if(p==0||p==1)
               return 1;
           return p*fac(p-1);
       }


        public static void main(String[] args) throws Exception {
            FastReader sc = new FastReader();

            Clock clock = new Clock();

            clock.start();
          int t1=sc.nextInt();
            for (int t = 0; t <t1; t++) {
                int n=sc.nextInt();
                int arr[][] = new int[n][3];
                for (int i = 0; i < n; i++) {
                    arr[i][0]=sc.nextInt();
                    arr[i][1]=sc.nextInt();
                    arr[i][2]=i;
                }
                int one=0;
                Arrays.sort(arr, new Comparator<int[]>() {
                    @Override
                    public int compare(int[] o1, int[] o2) {
                        if(o1[0]==o2[0])
                            return Integer.compare(o1[1],o2[1]);
                        return Integer.compare(o1[0],o2[0]);
                    }
                });
                int brr[]=new int[n];
                brr[arr[0][2]]=1;
                int k=1;
                for (int i = 1; i < n; i++) {
                    if(arr[i][0]<=arr[i-1][1])
                    {
                        brr[arr[i][2]]=k;
                        if(k==1)
                            ++one;
                        arr[i][0] =arr[i-1][0];
                        arr[i][1] = Math.max(arr[i][1],arr[i-1][1]);
                    }
                    else
                    {
                        if(k==1)
                            k=2;
                        else
                            k=1;
                        brr[arr[i][2]]=k;
                        if(k==1)
                            ++one;
                    }
                }
                if(one==n-1)
                {
                    out.println(-1);
                    continue;
                }
               // System.out.println(one);
                for (int i = 0; i < n; i++) {
                    out.print(brr[i]+" ");
                }
                out.println();


            }
            out.close();




        }
    }


    class Pair{

        int a,b;
        Pair(int a,int b)
        {
            this.a=a;
            this.b=b;
        }
    }
    class DSU
    {
        int parent[];
        int rank[];

        long sum[] ;
        DSU(int n)
        {
            this.parent=new int[n];
            this.rank=new int[n];
            sum=new long[n];
            Arrays.fill(parent,-1);
            Arrays.fill(rank,1);

        }

        int find(int s1)
        {
            if(parent[s1]==-1)
                return s1;
            return parent[s1]=find(parent[s1]);
        }

        void unite(int s1,int s2)
        {
            int p1=this.find(s1);
            int p2=this.find(s2);
            if(p1==p2)
                return;
            if(rank[p1]>rank[p2])
            {
                parent[p2]=p1;
                rank[p1]+=rank[p2];
                // System.out.println(arr[p2]);

                sum[p1]+=sum[p2];
                //sum[p2]+=sum[p1];

            }
            else
            {
                parent[p1]=p2;
                rank[p2]+=rank[p1];
                //System.out.println(arr[p1]);
                sum[p2]+=sum[p1];
                //sum[p1]+=sum[p2];
            }
        }


    }

    class Gaph {

        HashMap<Integer, ArrayList<Integer>> hm;

        Gaph() {
            hm = new HashMap<>();
        }

        Gaph(int n) {

            hm = new HashMap<>();
            for (int i = 0; i < n; i++) {
                hm.put(i, new ArrayList<Integer>());
            }
        }

        // function for adding an edge.................................................
        public void addEdge(int a, int b, boolean isDir) {
            if (isDir) {
                if (hm.containsKey(a)) {
                    hm.get(a).add(b);
                } else {
                    hm.put(a, new ArrayList<>(Arrays.asList(b)));
                }
            } else {
                if (hm.containsKey(a)) {
                    hm.get(a).add(b);
                } else if (!hm.containsKey(a)) {
                    hm.put(a, new ArrayList<>(Arrays.asList(b)));
                }

                if (hm.containsKey(b)) {
                    hm.get(b).add(a);
                } else if (!hm.containsKey(b)) {
                    hm.put(b, new ArrayList<>(Arrays.asList(a)));
                }
            }
        }


    }

    // out.println(al.toString().replaceAll("[\\[|\\]|,]",""));