BerPhone X is almost ready for release with n applications being preinstalled on the phone. A category of an application characterizes a genre or a theme of this application (like "game", "business", or "education"). The categories are given as integers between 1 and n, inclusive; the i-th application has category c_i. 

You can choose m — the number of screens and s — the size of each screen. You need to fit all n icons of the applications (one icon representing one application) meeting the following requirements:

  * On each screen, all the icons must belong to applications of the same category (but different screens can contain icons of applications of the same category); 
  * Each screen must be either completely filled with icons (the number of icons on the screen is equal to s) or almost filled with icons (the number of icons is equal to s-1). 



Your task is to find the minimal possible number of screens m.

Input

The first line contains an integer t (1 ≤ t ≤ 10 000) — the number of test cases in the input. Then t test cases follow.

The first line of each test case contains an integer n (1 ≤ n ≤ 2⋅10^6) — the number of the icons. The second line contains n integers c_1, c_2, ..., c_n (1 ≤ c_i ≤ n), where c_i is the category of the i-th application.

It is guaranteed that the sum of the values of n for all test cases in the input does not exceed 2⋅10^6.

Output

Print t integers — the answers to the given test cases in the order they follow in the input. The answer to a test case is an integer m — the minimum number of screens on which all n icons can be placed satisfying the given requirements.

Example

Input


3
11
1 5 1 5 1 5 1 1 1 1 5
6
1 2 2 2 2 1
5
4 3 3 1 2


Output


3
3
4

Note

In the first test case of the example, all the icons can be placed on three screens of size 4: a screen with 4 icons of the category 1, a screen with 3 icons of the category 1, and a screen with 4 icons of the category 5.
import java.io.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;

public class cf1267j {

    public static void main(String[] args) throws IOException {
        int t = ri();
        while (t --> 0) {
            int n = ri(), ind = 0;
            Map<Integer, Integer> map = new HashMap<>(), cnt = new HashMap<>();
            r();
            for (int i = 0; i < n; ++i) {
                int c = ni();
                if (!map.containsKey(c)) {
                    map.put(c, ind++);
                }
                cnt.put(map.get(c), cnt.getOrDefault(map.get(c), 0) + 1);
            }
            int min = IMAX;
            for (int i = 0; i < ind; ++i) {
                min = min(min, cnt.get(i));
            }
            int ans = IMAX;
            next: for (int i = min + 1; i >= 2; --i) {
                int x = 0;
                for (int j = 0; j < ind; ++j) {
                    int c = cnt.get(j);
                    if (c % i != 0 && c % (i - 1) != 0 && c / i == c / (i - 1)) {
                        continue next;
                    } else {
                        x += (c + i - 1) / i;
                    }
                }
                // prln(i, x);
                ans = min(ans, x);
            }
            prln(ans);
        }
        close();
    }

    static BufferedReader __in = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter __out = new PrintWriter(new OutputStreamWriter(System.out));
    static StringTokenizer input;
    static Random __rand = new Random();

    // references
    // IBIG = 1e9 + 7
    // IMAX ~= 2e10
    // LMAX ~= 9e18
    
    // constants
    static final int IBIG = 1000000007;
    static final int IMAX = 2147483647;
    static final int IMIN = -2147483648;
    static final long LMAX = 9223372036854775807L;
    static final long LMIN = -9223372036854775808L;
    // math util
    static int minof(int a, int b, int c) {return min(a, min(b, c));}
    static int minof(int... x) {if(x.length == 1) return x[0]; if(x.length == 2) return min(x[0], x[1]); if(x.length == 3) return min(x[0], min(x[1], x[2])); int min = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] < min) min = x[i]; return min;}
    static long minof(long a, long b, long c) {return min(a, min(b, c));}
    static long minof(long... x) {if(x.length == 1) return x[0]; if(x.length == 2) return min(x[0], x[1]); if(x.length == 3) return min(x[0], min(x[1], x[2])); long min = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] < min) min = x[i]; return min;}
    static int maxof(int a, int b, int c) {return max(a, max(b, c));}
    static int maxof(int... x) {if(x.length == 1) return x[0]; if(x.length == 2) return max(x[0], x[1]); if(x.length == 3) return max(x[0], max(x[1], x[2])); int max = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] > max) max = x[i]; return max;}
    static long maxof(long a, long b, long c) {return max(a, max(b, c));}
    static long maxof(long... x) {if(x.length == 1) return x[0]; if(x.length == 2) return max(x[0], x[1]); if(x.length == 3) return max(x[0], max(x[1], x[2])); long max = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] > max) max = x[i]; return max;}
    static int powi(int a, int b) {if(a == 0) return 0; int ans = 1; while(b > 0) {if((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static long powl(long a, int b) {if(a == 0) return 0; long ans = 1; while(b > 0) {if((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static int fli(double d) {return (int)d;}
    static int cei(double d) {return (int)ceil(d);}
    static long fll(double d) {return (long)d;}
    static long cel(double d) {return (long)ceil(d);}
    static int gcf(int a, int b) {return b == 0 ? a : gcf(b, a % b);}
    static long gcf(long a, long b) {return b == 0 ? a : gcf(b, a % b);}
    static int randInt(int min, int max) {return __rand.nextInt(max - min + 1) + min;}
    static long hash(long x) {x += 0x9e3779b97f4a7c15L; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9L; x = (x ^ (x >> 27)) * 0x94d049bb133111ebL; return x ^ (x >> 31);}
    // array util
    static void reverse(int[] a) {for(int i = 0, n = a.length, half = n / 2; i < half; ++i) {int swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(long[] a) {for(int i = 0, n = a.length, half = n / 2; i < half; ++i) {long swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(char[] a) {for(int i = 0, n = a.length, half = n / 2; i < half; ++i) {char swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void shuffle(int[] a) {int n = a.length - 1; for(int i = 0; i < n; ++i) {int ind = randInt(i, n); int swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void shuffle(long[] a) {int n = a.length - 1; for(int i = 0; i < n; ++i) {int ind = randInt(i, n); long swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void rsort(int[] a) {shuffle(a); sort(a);}
    static void rsort(long[] a) {shuffle(a); sort(a);}
    static int[] copy(int[] a) {int[] ans = new int[a.length]; for(int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static long[] copy(long[] a) {long[] ans = new long[a.length]; for(int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static char[] copy(char[] a) {char[] ans = new char[a.length]; for(int i = 0; i < a.length; ++i) ans[i] = a[i]; return ans;}
    static int[] sorted(int[] a) {int[] ans = copy(a); sort(ans); return ans;}
    static long[] sorted(long[] a) {long[] ans = copy(a); sort(ans); return ans;}
    static int[] rsorted(int[] a) {int[] ans = copy(a); rsort(ans); return ans;}
    static long[] rsorted(long[] a) {long[] ans = copy(a); rsort(ans); return ans;}
    // graph util
    static List<List<Integer>> graph(int n) {List<List<Integer>> g = new ArrayList<>(); for(int i = 0; i < n; ++i) g.add(new ArrayList<>()); return g;}
    static List<List<Integer>> graph(List<List<Integer>> g, int m) throws IOException {for(int i = 0; i < m; ++i) connect(g, rni() - 1, ni() - 1); return g;}
    static List<List<Integer>> graph(int n, int m) throws IOException {return graph(graph(n), m);}
    static List<List<Integer>> dgraph(List<List<Integer>> g, int m) throws IOException {for(int i = 0; i < m; ++i) connecto(g, rni() - 1, ni() - 1); return g;}
    static List<List<Integer>> dgraph(List<List<Integer>> g, int n, int m) throws IOException {return dgraph(graph(n), m);}
    static List<Set<Integer>> sgraph(int n) {List<Set<Integer>> g = new ArrayList<>(); for(int i = 0; i < n; ++i) g.add(new HashSet<>()); return g;}
    static List<Set<Integer>> sgraph(List<Set<Integer>> g, int m) throws IOException {for(int i = 0; i < m; ++i) connect(g, rni() - 1, ni() - 1); return g;}
    static List<Set<Integer>> sgraph(int n, int m) throws IOException {return sgraph(sgraph(n), m);}
    static List<Set<Integer>> dsgraph(List<Set<Integer>> g, int m) throws IOException {for(int i = 0; i < m; ++i) connecto(g, rni() - 1, ni() - 1); return g;}
    static List<Set<Integer>> dsgraph(List<Set<Integer>> g, int n, int m) throws IOException {return dsgraph(sgraph(n), m);}
    static void connect(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).add(v); g.get(v).add(u);}
    static void connecto(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).add(v);}
    static void dconnect(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).remove(v); g.get(v).remove(u);}
    static void dconnecto(List<? extends Collection<Integer>> g, int u, int v) {g.get(u).remove(v);}
    // input
    static void r() throws IOException {input = new StringTokenizer(__in.readLine());}
    static int ri() throws IOException {return Integer.parseInt(__in.readLine());}
    static long rl() throws IOException {return Long.parseLong(__in.readLine());}
    static int[] ria(int n) throws IOException {int[] a = new int[n]; input = new StringTokenizer(__in.readLine()); for(int i = 0; i < n; ++i) a[i] = Integer.parseInt(input.nextToken()); return a;}
    static int[] riam1(int n) throws IOException {int[] a = new int[n]; input = new StringTokenizer(__in.readLine()); for(int i = 0; i < n; ++i) a[i] = Integer.parseInt(input.nextToken()) - 1; return a;}
    static long[] rla(int n) throws IOException {long[] a = new long[n]; input = new StringTokenizer(__in.readLine()); for(int i = 0; i < n; ++i) a[i] = Long.parseLong(input.nextToken()); return a;}
    static char[] rcha() throws IOException {return __in.readLine().toCharArray();}
    static String rline() throws IOException {return __in.readLine();}
    static int rni() throws IOException {input = new StringTokenizer(__in.readLine()); return Integer.parseInt(input.nextToken());}
    static int ni() {return Integer.parseInt(input.nextToken());}
    static long rnl() throws IOException {input = new StringTokenizer(__in.readLine()); return Long.parseLong(input.nextToken());}
    static long nl() {return Long.parseLong(input.nextToken());}
    // output
    static void pr(int i) {__out.print(i);}
    static void prln(int i) {__out.println(i);}
    static void pr(long l) {__out.print(l);}
    static void prln(long l) {__out.println(l);}
    static void pr(double d) {__out.print(d);}
    static void prln(double d) {__out.println(d);}
    static void pr(char c) {__out.print(c);}
    static void prln(char c) {__out.println(c);}
    static void pr(char[] s) {__out.print(new String(s));}
    static void prln(char[] s) {__out.println(new String(s));}
    static void pr(String s) {__out.print(s);}
    static void prln(String s) {__out.println(s);}
    static void pr(Object o) {__out.print(o);}
    static void prln(Object o) {__out.println(o);}
    static void prln() {__out.println();}
    static void pryes() {__out.println("yes");}
    static void pry() {__out.println("Yes");}
    static void prY() {__out.println("YES");}
    static void prno() {__out.println("no");}
    static void prn() {__out.println("No");}
    static void prN() {__out.println("NO");}
    static void pryesno(boolean b) {__out.println(b ? "yes" : "no");};
    static void pryn(boolean b) {__out.println(b ? "Yes" : "No");}
    static void prYN(boolean b) {__out.println(b ? "YES" : "NO");}
    static void prln(int... a) {for(int i = 0, len = a.length - 1; i < len; __out.print(a[i]), __out.print(' '), ++i); __out.println(a[a.length - 1]);}
    static void prln(long... a) {for(int i = 0, len = a.length - 1; i < len; __out.print(a[i]), __out.print(' '), ++i); __out.println(a[a.length - 1]);}
    static <T> void prln(Collection<T> c) {int n = c.size() - 1; Iterator<T> iter = c.iterator(); for(int i = 0; i < n; __out.print(iter.next()), __out.print(' '), ++i); if(n >= 0) __out.println(iter.next()); else __out.println();}
    static void h() {__out.println("hlfd");}
    static void flush() {__out.flush();}
    static void close() {__out.close();}
}