Problem: You are given an array a of n integers. Define the cost of some array t as follows:

$$$cost(t) = ∑_{x ∈ set(t) } last(x) - first(x),$$$ 

where set(t) is the set of all values in t without repetitions, first(x), and last(x) are the indices of the first and last occurrence of x in t, respectively. In other words, we compute the distance between the first and last occurrences for each distinct element and sum them up.

You need to split the array a into k consecutive segments such that each element of a belongs to exactly one segment and the sum of the cost of individual segments is minimum.

Input

The first line contains two integers n, k (1 ≤ n ≤ 35 000, 1 ≤ k ≤ min(n,100)).

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n).

Output

Output the minimum sum of the cost of individual segments.

Examples

Input


7 2
1 6 6 4 6 6 6


Output


3


Input


7 4
5 5 5 5 2 3 3


Output


1

Note

In the first example, we can divide the array into [1,6,6,4] and [6,6,6]. Cost of [1,6,6,4] will be (1-1) + (3 - 2) + (4-4) = 1 and cost of [6,6,6] will be 3-1 = 2. Total cost would be 1 + 2 = 3.

In the second example, divide the array into [5,5],[5],[5,2,3] and [3]. Total Cost would be 1 + 0 + 0 + 0 = 1.

Solution (in JAVA):

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

public class CF_1527_E{
    //SOLUTION BEGIN
    void pre() throws Exception{}
    void solve(int TC) throws Exception{
        int N = ni(), K = ni();
        int[] A = new int[1+N];
        int[] prevA = new int[1+N], prev = new int[1+N];
        Arrays.fill(prevA, -1);Arrays.fill(prev, -1);
        for(int i = 1; i<= N; i++){
            A[i] = ni();
            if(prevA[A[i]] != -1)
                prev[i] = prevA[A[i]];
            prevA[A[i]] = i;
        }
        long[] val = new long[1+N];
        Arrays.fill(val, IINF);
        val[0] = 0;
        for(int k = 1; k <= K; k++){
            LazySegmentTree lst = new LazySegmentTree(val);
            for(int i = 0; i<= N; i++){
                if(prev[i] != -1)
                    lst.update(0, prev[i]-1, i-prev[i]);
                val[i] = lst.min(0, i);
            }
        }
        pn(val[N]);
    }
    class LazySegmentTree{
        int m = 1;
        long[] t, lazy;
        public LazySegmentTree(long[] v){
            while(m<v.length)m<<=1;
            t = new long[m<<1];
            lazy = new long[m<<1];
            Arrays.fill(t, IINF);
            for(int i = 0; i< v.length; i++)t[i+m] = v[i];
            for(int i = m-1; i> 0; i--)t[i] = Math.min(t[i<<1], t[i<<1|1]);
        }
        private void push(int i){
            if(lazy[i] != 0){
                t[i] += lazy[i];
                if(i < m){
                    lazy[i<<1] += lazy[i];
                    lazy[i<<1|1] += lazy[i];
                }
                lazy[i] = 0;
            }
        }
        public void update(int l, int r, long x){u(l, r, 0, m-1, 1, x);}
        public long min(int l, int r){return s(l, r, 0, m-1, 1);}

        private void u(int l, int r, int ll, int rr, int i, long x){
            push(i);
            if(l == ll && r == rr){
                lazy[i] += x;
                push(i);return;
            }
            int mid = (ll+rr)/2;
            if(r <= mid){
                u(l, r, ll, mid, i<<1, x);
                push(i<<1|1);
            }else if(l > mid){
                push(i<<1);
                u(l, r, mid+1, rr, i<<1|1, x);
            }else{
                u(l, mid, ll, mid, i<<1, x);
                u(mid+1, r, mid+1, rr, i<<1|1, x);
            }
            t[i] = Math.min(t[i<<1], t[i<<1|1]);
        }
        private long s(int l, int r, int ll, int rr, int i){
            push(i);
            if(l == ll && r == rr)return t[i];
            int mid = (ll+rr)/2;
            if(r <= mid)return s(l ,r, ll, mid, i<<1);
            else if(l > mid)return s(l, r, mid+1, rr, i<<1|1);
            else return Math.min(s(l, mid, ll, mid, i<<1), s(mid+1, r, mid+1, rr, i<<1|1));
        }
    }
    //SOLUTION END
    void hold(boolean b)throws Exception{if(!b)throw new Exception("Hold right there, Sparky!");}
    void exit(boolean b){if(!b)System.exit(0);}
    static void dbg(Object... o){System.err.println(Arrays.deepToString(o));}
    final long IINF = (long)1e17;
    final int INF = (int)1e9+2;
    DecimalFormat df = new DecimalFormat("0.00000000000");
    double PI = 3.141592653589793238462643383279502884197169399, eps = 1e-8;
    static boolean multipleTC = false, memory = true, fileIO = false;
    FastReader in;PrintWriter out;
    void run() throws Exception{
        long ct = System.currentTimeMillis();
        if (fileIO) {
            in = new FastReader("");
            out = new PrintWriter("");
        } else {
            in = new FastReader();
            out = new PrintWriter(System.out);
        }
        //Solution Credits: Taranpreet Singh
        int T = multipleTC? ni():1;
        pre();
        for (int t = 1; t <= T; t++) solve(t);
        out.flush();
        out.close();
        System.err.println(System.currentTimeMillis() - ct);
    }
    public static void main(String[] args) throws Exception{
        if(memory)new Thread(null, new Runnable() {public void run(){try{new CF_1527_E().run();}catch(Exception e){e.printStackTrace();System.exit(1);}}}, "1", 1 << 28).start();
        else new CF_1527_E().run();
    }
    int[][] make(int n, int e, int[] from, int[] to, boolean f){
        int[][] g = new int[n][];int[]cnt = new int[n];
        for(int i = 0; i< e; i++){
            cnt[from[i]]++;
            if(f)cnt[to[i]]++;
        }
        for(int i = 0; i< n; i++)g[i] = new int[cnt[i]];
        for(int i = 0; i< e; i++){
            g[from[i]][--cnt[from[i]]] = to[i];
            if(f)g[to[i]][--cnt[to[i]]] = from[i];
        }
        return g;
    }
    int[][][] makeS(int n, int e, int[] from, int[] to, boolean f){
        int[][][] g = new int[n][][];int[]cnt = new int[n];
        for(int i = 0; i< e; i++){
            cnt[from[i]]++;
            if(f)cnt[to[i]]++;
        }
        for(int i = 0; i< n; i++)g[i] = new int[cnt[i]][];
        for(int i = 0; i< e; i++){
            g[from[i]][--cnt[from[i]]] = new int[]{to[i], i, 0};
            if(f)g[to[i]][--cnt[to[i]]] = new int[]{from[i], i, 1};
        }
        return g;
    }
    int find(int[] set, int u){return set[u] = (set[u] == u?u:find(set, set[u]));}
    int digit(long s){int ans = 0;while(s>0){s/=10;ans++;}return ans;}
    long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
    int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
    int bit(long n){return (n==0)?0:(1+bit(n&(n-1)));}
    void p(Object... o){for(Object oo:o)out.print(oo+" ");}
    void pn(Object... o){for(int i = 0; i< o.length; i++)out.print(o[i]+(i+1 < o.length?" ":"\n"));}
    void pni(Object... o){for(Object oo:o)out.print(oo+" ");out.println();out.flush();}
    String n()throws Exception{return in.next();}
    String nln()throws Exception{return in.nextLine();}
    int ni()throws Exception{return Integer.parseInt(in.next());}
    long nl()throws Exception{return Long.parseLong(in.next());}
    double nd()throws Exception{return Double.parseDouble(in.next());}

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

        public FastReader(String s) throws Exception{
            br = new BufferedReader(new FileReader(s));
        }

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

        String nextLine() throws Exception{
            String str;
            try{
                str = br.readLine();
            }catch (IOException e){
                throw new Exception(e.toString());
            }
            return str;
        }
    }
}