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;

# define Rep(i,a,b) for(int i=a;i<=b;i++)
# define _Rep(i,a,b) for(int i=a;i>=b;i--)
# define RepG(i,u) for(int i=head[u];~i;i=e[i].next)

typedef long long ll;

const int N=3.5e4+5;
const int M=105;

template<typename T> void read(T &x){
    x=0;int f=1;
    char c=getchar();
    for(;!isdigit(c);c=getchar())if(c=='-')f=-1;
    for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+c-'0';
    x*=f;
}

int n,m;
ll f[N];
int a[N],lst[N],pre[N];

struct node{
    ll min,tag;
}seg[N<<2];

# define lc (u<<1)
# define rc (u<<1|1)

void pushup(int u){
    seg[u].min=min(seg[lc].min,seg[rc].min);
}

void renew(int u,int k){
    seg[u].min+=k;
    seg[u].tag+=k;
}

void pushdown(int u){
    renew(lc,seg[u].tag);
    renew(rc,seg[u].tag);
    seg[u].tag=0;
}

void build(int u,int l,int r){
    seg[u].tag=0;
    if(l==r){
        seg[u].min=f[l-1];
        return;
    }
    int mid=l+r>>1;
    build(lc,l,mid);
    build(rc,mid+1,r);
    pushup(u);
}

void update(int u,int l,int r,int ql,int qr,int k){
    if(l>=ql&&r<=qr){
        renew(u,k);
        return;
    }
    if(seg[u].tag)pushdown(u);
    int mid=l+r>>1;
    if(ql<=mid)update(lc,l,mid,ql,qr,k);
    if(qr>mid)update(rc,mid+1,r,ql,qr,k);
    pushup(u);
}

int main()
{
    # ifdef hibike
    freopen("testdata.in","r",stdin);
    freopen("test1.out","w",stdout);
    # endif
    memset(f,0x3f,sizeof(f));
    read(n),read(m);
    Rep(i,1,n)read(a[i]);
    Rep(i,1,n)pre[i]=lst[a[i]],lst[a[i]]=i;
    f[0]=0;
    Rep(j,1,m){
        build(1,1,n);
        Rep(i,1,n){
            if(pre[i])update(1,1,n,1,pre[i],i-pre[i]);
            f[i]=seg[1].min;
        }
    }
    printf("%lld\n",f[n]);
    return 0;
}