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 CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
const int N=3e4+5e3+100;
#define mid (l+r)/2
#define lson k<<1,l,mid
#define inf 0x3f3f3f3f
#define rson k<<1|1,mid+1,r
int a[N],pre[N],pos[N];
int dp[105][N];
struct node{
	int sum,lazy;
}t[N<<2];
void build(int k,int l,int r,int op)
{
	t[k].lazy=0;
	if(l==r)
	{
		t[k].sum=dp[op][l];
		return ;
	}
	build(lson,op);
	build(rson,op);
	t[k].sum=min(t[k<<1].sum,t[k<<1|1].sum);
}
void pushdown(int k)
{
	if(t[k].lazy==0)return ;
	t[k<<1].lazy+=t[k].lazy;
	t[k<<1|1].lazy+=t[k].lazy;
	t[k<<1].sum+=t[k].lazy;
	t[k<<1|1].sum+=t[k].lazy;
	t[k].lazy=0;
}
void update(int k,int l,int r,int x,int y,int val)
{
	if(x<=l&&r<=y)
	{
		t[k].sum+=val;
		t[k].lazy+=val;
		return ;
	}
	pushdown(k);
	if(x<=mid)update(lson,x,y,val);
	if(y>mid)update(rson,x,y,val);
	t[k].sum=min(t[k<<1].sum,t[k<<1|1].sum);
}
int query(int k,int l,int r,int x,int y)
{
	if(x<=l&&r<=y)
	{
		return t[k].sum;
	}
	int ans=inf;
	if(x<=mid)ans=query(lson,x,y);
	if(y>mid)ans=min(ans,query(rson,x,y));
	return ans;
}
int main()
{
	int n,k;
	scanf("%d%d",&n,&k);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		if(pos[a[i]]==0)pre[i]=i;
		else pre[i]=pos[a[i]];
		pos[a[i]]=i;
		dp[1][i]=dp[1][i-1]+i-pre[i];
	}
	for(int i=2;i<=k;i++)
	{
		build(1,0,n,i-1);
		for(int j=1;j<=n;j++)
		{
			update(1,0,n,0,pre[j]-1,j-pre[j]);
			dp[i][j]=query(1,0,n,0,j-1);
		}
	}
	printf("%d\n",dp[k][n]);
}