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.io.*;
import java.util.*;

public class E5 {
	InputStream is;
	FastWriter out;
	String INPUT = "";

	void solve()
	{
		int n = ni();
		int K = ni();
		int[] a = na(n);

		long[] dp = new long[n+1];
		Arrays.fill(dp, Long.MAX_VALUE / 2);
		dp[0] = 0;

		int[] prev = new int[n];
		Map<Integer, Integer> pmap = new HashMap<>();
		for(int i = 0;i < n;i++){
			prev[i] = pmap.getOrDefault(a[i], -1);
			pmap.put(a[i], i);
		}

		for(int i = 0;i < K;i++){
			long[] ndp = new long[n+1];
			Arrays.fill(ndp, Long.MAX_VALUE / 2);
			StarrySkyTreeL sst = new StarrySkyTreeL(dp);
			for(int j = 1;j <= n;j++){
				int pr = prev[j-1];
				if(pr != -1)sst.add(0, pr+1, j-1-pr);
				ndp[j] = sst.min(0, j);
			}
			dp = ndp;
		}
		out.println(dp[n]);
	}

	public class StarrySkyTreeL {
		public final int M, H, N, LH;
		public long[] mins;
		public long[] plus;
		public static final long I = Long.MAX_VALUE/4; // I+plus<long

		public StarrySkyTreeL(int n)
		{
			N = n;
			M = Integer.highestOneBit(Math.max(n-1, 1))<<2;
			H = M>>>1;
			LH = Integer.numberOfTrailingZeros(H);
			mins = new long[M];
			plus = new long[H];
		}

		public StarrySkyTreeL(long[] a)
		{
			this(a.length);
			for(int i = 0;i < N;i++){
				mins[H+i] = a[i];
			}
			Arrays.fill(mins, H+N, M, I);
			for(int i = H-1;i >= 1;i--)propagate(i);
		}

		private void push1(int cur)
		{
			if(plus[cur] == 0)return;
			int L = cur*2, R = L + 1;
			mins[L] += plus[cur];
			mins[R] += plus[cur];
			if(L < H){
				plus[L] += plus[cur];
				plus[R] += plus[cur];
			}
			plus[cur] = 0;
		}

		private void propagate(int i)
		{
			mins[i] = Math.min(mins[2*i], mins[2*i+1]) + plus[i];
		}

		private void add1(int cur, long v)
		{
			mins[cur] += v;
			if(cur < H){
				plus[cur] += v;
			}
		}

		private void push(int l, int r)
		{
			for(int i = LH;i >= 1;i--) {
				if (l >>> i << i != l) push1(l >>> i);
				if (r >>> i << i != r) push1(r >>> i);
			}
		}

		public void add(int l, int r, long v)
		{
			if(l >= r)return;
			l += H; r += H;
			push(l, r);
			for(int ll = l, rr = r;ll < rr;ll>>>=1,rr>>>=1){
				if((ll&1) == 1) add1(ll++, v);
				if((rr&1) == 1) add1(--rr, v);
			}
			for(int i = 1;i <= LH;i++){
				if(l>>>i<<i != l)propagate(l>>>i);
				if(r>>>i<<i != r)propagate(r>>>i);
			}
		}

		public long min(int l, int r){
			long min = I;
			if(l >= r)return min;
			l += H; r += H;
			push(l, r);
			for(;l < r;l>>>=1,r>>>=1){
				if((l&1) == 1)min = Math.min(min, mins[l++]);
				if((r&1) == 1)min = Math.min(min, mins[--r]);
			}
			return min;
		}

		public int firstle(int l, long v) {
			if(l >= H)return -1;
			int cur = H+l;
			for(int i = 1, j = Integer.numberOfTrailingZeros(H)-1;i <= cur;j--){
				push1(i);
				i = i*2|cur>>>j&1;
			}
			while(true){
				push1(cur);
				if(mins[cur] <= v){
					if(cur >= H)return cur-H;
					cur = 2*cur;
				}else{
					cur++;
					if((cur&cur-1) == 0)return -1;
					cur = cur>>>Integer.numberOfTrailingZeros(cur);
				}
			}
		}

		public int lastle(int l, long v) {
			if(l < 0)return -1;
			int cur = H+l;
			for(int i = 1, j = Integer.numberOfTrailingZeros(H)-1;i <= cur;j--){
				push1(i);
				i = i*2|cur>>>j&1;
			}
			while(true){
				push1(cur);
				if(mins[cur] <= v){
					if(cur >= H)return cur-H;
					cur = 2*cur+1;
				}else{
					if((cur&cur-1) == 0)return -1;
					cur = cur>>>Integer.numberOfTrailingZeros(cur);
					cur--;
				}
			}
		}

		public long[] toArray() { return toArray(1, 0, H, new long[H]); }

		private long[] toArray(int cur, int l, int r, long[] ret)
		{
			if(r-l == 1){
				ret[cur-H] = mins[cur];
			}else{
				toArray(2*cur, l, l+r>>>1, ret);
				toArray(2*cur+1, l+r>>>1, r, ret);
				for(int i = l;i < r;i++)ret[i] += plus[cur];
			}
			return ret;
		}
	}


	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new FastWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new E5().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

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

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

	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}

	private int[][] nmi(int n, int m) {
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = na(m);
		return map;
	}

	private int ni() { return (int)nl(); }

	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}

		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	public static class FastWriter
	{
		private static final int BUF_SIZE = 1<<13;
		private final byte[] buf = new byte[BUF_SIZE];
		private final OutputStream out;
		private int ptr = 0;

		private FastWriter(){out = null;}

		public FastWriter(OutputStream os)
		{
			this.out = os;
		}

		public FastWriter(String path)
		{
			try {
				this.out = new FileOutputStream(path);
			} catch (FileNotFoundException e) {
				throw new RuntimeException("FastWriter");
			}
		}

		public FastWriter write(byte b)
		{
			buf[ptr++] = b;
			if(ptr == BUF_SIZE)innerflush();
			return this;
		}

		public FastWriter write(char c)
		{
			return write((byte)c);
		}

		public FastWriter write(char[] s)
		{
			for(char c : s){
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			}
			return this;
		}

		public FastWriter write(String s)
		{
			s.chars().forEach(c -> {
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			});
			return this;
		}

		private static int countDigits(int l) {
			if (l >= 1000000000) return 10;
			if (l >= 100000000) return 9;
			if (l >= 10000000) return 8;
			if (l >= 1000000) return 7;
			if (l >= 100000) return 6;
			if (l >= 10000) return 5;
			if (l >= 1000) return 4;
			if (l >= 100) return 3;
			if (l >= 10) return 2;
			return 1;
		}

		public FastWriter write(int x)
		{
			if(x == Integer.MIN_VALUE){
				return write((long)x);
			}
			if(ptr + 12 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		private static int countDigits(long l) {
			if (l >= 1000000000000000000L) return 19;
			if (l >= 100000000000000000L) return 18;
			if (l >= 10000000000000000L) return 17;
			if (l >= 1000000000000000L) return 16;
			if (l >= 100000000000000L) return 15;
			if (l >= 10000000000000L) return 14;
			if (l >= 1000000000000L) return 13;
			if (l >= 100000000000L) return 12;
			if (l >= 10000000000L) return 11;
			if (l >= 1000000000L) return 10;
			if (l >= 100000000L) return 9;
			if (l >= 10000000L) return 8;
			if (l >= 1000000L) return 7;
			if (l >= 100000L) return 6;
			if (l >= 10000L) return 5;
			if (l >= 1000L) return 4;
			if (l >= 100L) return 3;
			if (l >= 10L) return 2;
			return 1;
		}

		public FastWriter write(long x)
		{
			if(x == Long.MIN_VALUE){
				return write("" + x);
			}
			if(ptr + 21 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		public FastWriter write(double x, int precision)
		{
			if(x < 0){
				write('-');
				x = -x;
			}
			x += Math.pow(10, -precision)/2;
			//		if(x < 0){ x = 0; }
			write((long)x).write(".");
			x -= (long)x;
			for(int i = 0;i < precision;i++){
				x *= 10;
				write((char)('0'+(int)x));
				x -= (int)x;
			}
			return this;
		}

		public FastWriter writeln(char c){
			return write(c).writeln();
		}

		public FastWriter writeln(int x){
			return write(x).writeln();
		}

		public FastWriter writeln(long x){
			return write(x).writeln();
		}

		public FastWriter writeln(double x, int precision){
			return write(x, precision).writeln();
		}

		public FastWriter write(int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter write(long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter writeln()
		{
			return write((byte)'\n');
		}

		public FastWriter writeln(int... xs)
		{
			return write(xs).writeln();
		}

		public FastWriter writeln(long... xs)
		{
			return write(xs).writeln();
		}

		public FastWriter writeln(char[] line)
		{
			return write(line).writeln();
		}

		public FastWriter writeln(char[]... map)
		{
			for(char[] line : map)write(line).writeln();
			return this;
		}

		public FastWriter writeln(String s)
		{
			return write(s).writeln();
		}

		private void innerflush()
		{
			try {
				out.write(buf, 0, ptr);
				ptr = 0;
			} catch (IOException e) {
				throw new RuntimeException("innerflush");
			}
		}

		public void flush()
		{
			innerflush();
			try {
				out.flush();
			} catch (IOException e) {
				throw new RuntimeException("flush");
			}
		}

		public FastWriter print(byte b) { return write(b); }
		public FastWriter print(char c) { return write(c); }
		public FastWriter print(char[] s) { return write(s); }
		public FastWriter print(String s) { return write(s); }
		public FastWriter print(int x) { return write(x); }
		public FastWriter print(long x) { return write(x); }
		public FastWriter print(double x, int precision) { return write(x, precision); }
		public FastWriter println(char c){ return writeln(c); }
		public FastWriter println(int x){ return writeln(x); }
		public FastWriter println(long x){ return writeln(x); }
		public FastWriter println(double x, int precision){ return writeln(x, precision); }
		public FastWriter print(int... xs) { return write(xs); }
		public FastWriter print(long... xs) { return write(xs); }
		public FastWriter println(int... xs) { return writeln(xs); }
		public FastWriter println(long... xs) { return writeln(xs); }
		public FastWriter println(char[] line) { return writeln(line); }
		public FastWriter println(char[]... map) { return writeln(map); }
		public FastWriter println(String s) { return writeln(s); }
		public FastWriter println() { return writeln(); }
	}

	public void trnz(int... o)
	{
		for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
		System.out.println();
	}

	// print ids which are 1
	public void trt(long... o)
	{
		Queue<Integer> stands = new ArrayDeque<>();
		for(int i = 0;i < o.length;i++){
			for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
		}
		System.out.println(stands);
	}

	public void tf(boolean... r)
	{
		for(boolean x : r)System.out.print(x?'#':'.');
		System.out.println();
	}

	public void tf(boolean[]... b)
	{
		for(boolean[] r : b) {
			for(boolean x : r)System.out.print(x?'#':'.');
			System.out.println();
		}
		System.out.println();
	}

	public void tf(long[]... b)
	{
		if(INPUT.length() != 0) {
			for (long[] r : b) {
				for (long x : r) {
					for (int i = 0; i < 64; i++) {
						System.out.print(x << ~i < 0 ? '#' : '.');
					}
				}
				System.out.println();
			}
			System.out.println();
		}
	}

	public void tf(long... b)
	{
		if(INPUT.length() != 0) {
			for (long x : b) {
				for (int i = 0; i < 64; i++) {
					System.out.print(x << ~i < 0 ? '#' : '.');
				}
			}
			System.out.println();
		}
	}

	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}