Problem: The round carousel consists of n figures of animals. Figures are numbered from 1 to n in order of the carousel moving. Thus, after the n-th figure the figure with the number 1 follows. Each figure has its own type — the type of the animal corresponding to this figure (the horse, the tiger and so on). The type of animal of the i-th figure equals t_i.

<image> The example of the carousel for n=9 and t=[5, 5, 1, 15, 1, 5, 5, 1, 1]. 

You want to color each figure in one of the colors. You think that it's boring if the carousel contains two different figures (with the distinct types of animals) going one right after another and colored in the same color.

Your task is to color the figures in such a way that the number of distinct colors used is the minimum possible and there are no figures of the different types going one right after another and colored in the same color. If you use exactly k distinct colors, then the colors of figures should be denoted with integers from 1 to k.

Input

The input contains one or more test cases.

The first line contains one integer q (1 ≤ q ≤ 10^4) — the number of test cases in the test. Then q test cases follow. One test case is given on two lines.

The first line of the test case contains one integer n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of figures in the carousel. Figures are numbered from 1 to n in order of carousel moving. Assume that after the n-th figure the figure 1 goes.

The second line of the test case contains n integers t_1, t_2, ..., t_n (1 ≤ t_i ≤ 2 ⋅ 10^5), where t_i is the type of the animal of the i-th figure.

The sum of n over all test cases does not exceed 2⋅10^5.

Output

Print q answers, for each test case print two lines.

In the first line print one integer k — the minimum possible number of distinct colors of figures.

In the second line print n integers c_1, c_2, ..., c_n (1 ≤ c_i ≤ k), where c_i is the color of the i-th figure. If there are several answers, you can print any.

Example

Input


4
5
1 2 1 2 2
6
1 2 2 1 2 2
5
1 2 1 2 3
3
10 10 10


Output


2
1 2 1 2 2
2
2 1 2 1 2 1
3
2 3 2 3 1
1
1 1 1 

Solution (in JAVA):

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

import static java.lang.Double.parseDouble;
import static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;
import static java.lang.Math.abs;
import static java.lang.System.exit;

public class Main {

    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;

    int n, a[], dp[][];

    boolean dp(int i, int lastColor) {
        if (i == n) return a[n - 1] == a[0] || lastColor != 0;
        if (dp[lastColor][i] != -1) return dp[lastColor][i] == 1;
        boolean ans = false;
        ans |= dp(i + 1, lastColor ^ 1);
        if (a[i] == a[i - 1])
            ans |= dp(i + 1, lastColor);
        dp[lastColor][i] = ans ? 1 : 0;
        return ans;
    }

    void Case() throws IOException {
        n = nextInt();
        a = na(n);
        dp = new int[2][n];
        Arrays.fill(dp[0], -1);
        Arrays.fill(dp[1], -1);
        if (Arrays.stream(a).distinct().count() == 1) {
            out.println(1);
            for (int i = 0; i < n; i++) out.print("1 ");
        } else if (dp(1, 0)) {
            out.println(2);
            if (n % 2 == 0) {
                for (int i = 0; i < n; i++) out.print(i % 2 + 1 + " ");
            } else {
                for (int i = 1; i < n; i++) {
                    if (a[i] == a[i - 1]) {
                        int c = 0, ans[] = new int[n];
                        for (int j = i - 1; j >= 0; j--) {
                            ans[j] = c;
                            c ^= 1;
                        }
                        c = 0;
                        for (int j = i; j < n; j++) {
                            ans[j] = c;
                            c ^= 1;
                        }
                        for (int x : ans) out.print(x + 1 + " ");
                        return;
                    }
                }
                if(a[0] == a[n-1]) {
                    int c = 0, ans[] = new int[n];
                    c = 0;
                    for (int j = 0; j < n - 1; j++) {
                        ans[j] = c;
                        c ^= 1;
                    }
                    for (int x : ans) out.print(x + 1 + " ");
                }
            }
        } else {
            out.println(3);
            for (int i = 0; i < n - 1; i++) out.print(i % 2 + 1 + " ");
            out.print(3);
        }
        out.println();
    }

    void solve() throws Exception {
        int t = nextInt();
        while (t-- > 0) Case();
    }


    // call it like this: lower_bound(a, x + 1) ( /!\ + 1 )
    public static int lower_bound(int[] a, int v) {
        int low = -1, high = a.length;
        while (high - low > 1) {
            int h = high + low >>> 1;
            if (a[h] >= v) {
                high = h;
            } else {
                low = h;
            }
        }
        return high;
    }

    private String getFraction(int a, int b) {
        assert b != 0;
        String sign = (a > 0 && b > 0) || (a < 0) && (b < 0) ? "+" : "-";
        a = abs(a);
        b = abs(b);
        int gcd = gcd(a, b);
        return sign + (a / gcd) + "/" + (b / gcd);
    }

    private int gcd(int a, int b) {
        while (b > 0) {
            int temp = b;
            b = a % b;
            a = temp;
        }
        return a;
    }

    private int lcm(int a, int b) {
        return a * (b / gcd(a, b));
    }

    public static int[] radixSort(int[] f) {
        if (f.length < 100) {
            Arrays.sort(f);
            return f;
        }
        int[] to = new int[f.length];
        {
            int[] b = new int[65537];
            for (int i = 0; i < f.length; i++) b[1 + (f[i] & 0xffff)]++;
            for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
            for (int i = 0; i < f.length; i++) to[b[f[i] & 0xffff]++] = f[i];
            int[] d = f;
            f = to;
            to = d;
        }
        {
            int[] b = new int[65537];
            for (int i = 0; i < f.length; i++) b[1 + (f[i] >>> 16)]++;
            for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
            for (int i = 0; i < f.length; i++) to[b[f[i] >>> 16]++] = f[i];
            int[] d = f;
            f = to;
            to = d;
        }
        return f;
    }

    // return all subsets in range 0..n-1 [ {0}, {1,4}, {2, 5}, ..., {1,2,..,n}, {n} ]
    List<List<Integer>> gen_subsets(int n) {
        List<List<Integer>> h = new ArrayList<>();
        for (int mask = 0; mask < (1 << n); mask++) {
            List<Integer> tmp = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                if ((mask & (1 << i)) != 0) {
                    tmp.add(i);
                }
            }
            h.add(tmp);
        }
        return h;
    }

    public static long pow(long a, long n, long mod) {
        long ret = 1;
        int x = 63 - Long.numberOfLeadingZeros(n);
        for (; x >= 0; x--) {
            ret = ret * ret % mod;
            if (n << 63 - x < 0)
                ret = ret * a % mod;
        }
        return ret;
    }

    class BIT {
        int BITree[];

        public BIT(int n) {
            BITree = new int[n + 1];
            for (int i = 1; i <= n; i++)
                BITree[i] = 0;
        }

        // sum [l, r]
        int getSum(int l, int r) {
            return getSum(r) - getSum(l - 1);
        }

        // sum [0, index]
        int getSum(int index) {
            int sum = 0;
            index = index + 1;
            while (index > 0) {
                sum += BITree[index];
                index -= index & (-index);
            }
            return sum;
        }

        // add val to range [l, r]
        void updateRange(int n, int val, int l, int r) {
            updateBIT(n, l, val);
            updateBIT(n, r + 1, -val);
        }

        void updateBIT(int n, int index, int val) {
            index = index + 1;
            while (index <= n) {
                BITree[index] += val;
                index += index & (-index);
            }
        }
    }

    public static boolean nextPermutation(Integer[] a) {
        int n = a.length;
        int i;
        for (i = n - 2; i >= 0 && a[i] >= a[i + 1]; i--) ;
        if (i == -1)
            return false;
        int j;
        for (j = i + 1; j < n && a[i] < a[j]; j++) ;
        int d = a[i];
        a[i] = a[j - 1];
        a[j - 1] = d;
        for (int p = i + 1, q = n - 1; p < q; p++, q--) {
            d = a[p];
            a[p] = a[q];
            a[q] = d;
        }
        return true;
    }

    void print(Object x) {
        out.print(String.valueOf(x));
        out.flush();
    }

    void println(Object x) {
        out.println(String.valueOf(x));
        out.flush();
    }

    private class MapCount<K> {
        Map<K, Integer> map;

        MapCount() {
            map = new HashMap<>();
        }

        public void add(K key) {
            map.put(key, map.containsKey(key) ? map.get(key) + 1 : 1);
        }

        public Integer getCount(K key) {
            return map.getOrDefault(key, 0);
        }

        public Set<K> keySet() {
            return map.keySet();
        }
    }

    // for Map with custom key/value, override toString in your custom class
    void printMap(Map map) {
        if (map.keySet().size() == 0) return;
        Object firstValue = map.keySet().iterator().next();
        if (map.get(firstValue) instanceof Queue || map.get(firstValue) instanceof List) {
            for (Object key : map.keySet()) {
                out.print(String.valueOf(key) + ": ");
                Collection values = (Collection) map.get(key);
                for (Object value : values) out.print(String.valueOf(value) + " ");
                out.println();
            }
        } else if (map.get(firstValue).getClass().isArray()) {
            for (Object key : map.keySet()) {
                out.print(String.valueOf(key) + ": ");
                Object[] values = (Object[]) map.get(key);
                for (Object value : values) out.print(String.valueOf(value) + " ");
                out.println();
            }
        } else {
            for (Object key : map.keySet()) {
                out.println(String.valueOf(key) + ": " + map.get(key));
            }
        }
    }

    private int[] na(int n) throws IOException {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = nextInt();
        return a;
    }

    private long[] nal(int n) throws IOException {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = nextLong();
        return a;
    }

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

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

    double nextDouble() throws IOException {
        return parseDouble(next());
    }

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

    public static void main(String[] args) throws Exception {
        try {
            boolean isLocal = false;
            if (isLocal) {
                in = new BufferedReader(new FileReader("solution.in"));
                out = new PrintWriter(new BufferedWriter(new FileWriter("solution.out")));
            } else {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(new OutputStreamWriter(System.out));
            }

            //long lStartTime = System.currentTimeMillis();
            new Main().solve();
            //long lEndTime = System.currentTimeMillis();
            //out.println("Elapsed time in seconds: " + (double)(lEndTime - lStartTime) / 1000.0);
            in.close();
            out.close();
        } catch (Throwable e) {
            e.printStackTrace();
            exit(1);
        }
    }
}