#include <cstdio>
#include <algorithm>
using namespace std;
int a[35005],last[35005];
int dp[35005][105];
int tree[105][140005],lazy[105][140005];
void build(int id,int p,int l,int r)
{
    if(l==r)
    {
        tree[id][p]=dp[l-1][id];
        return;
    }
    int mid=(l+r)/2;
    build(id,p<<1,l,mid);
    build(id,p<<1|1,mid+1,r);
    tree[id][p]=min(tree[id][p<<1],tree[id][p<<1|1]);
}
void pushdown(int id,int p,int l,int r)
{
    if(lazy[id][p])
    {
        tree[id][p<<1]+=lazy[id][p];
        tree[id][p<<1|1]+=lazy[id][p];
        lazy[id][p<<1]+=lazy[id][p];
        lazy[id][p<<1|1]+=lazy[id][p];
        lazy[id][p]=0;
    }
}
void update(int id,int p,int l,int r,int ql,int qr,int d)
{
    if(ql==l&&qr==r)
    {
        tree[id][p]+=d;
        lazy[id][p]+=d;
        return;
    }
    pushdown(id,p,l,r);
    int mid=(l+r)/2;
    if(qr<=mid)
        update(id,p<<1,l,mid,ql,qr,d);
    else if(ql>mid)
        update(id,p<<1|1,mid+1,r,ql,qr,d);
    else
    {
        update(id,p<<1,l,mid,ql,mid,d);
        update(id,p<<1|1,mid+1,r,mid+1,qr,d);
    }
    tree[id][p]=min(tree[id][p<<1],tree[id][p<<1|1]);
}
int query(int id,int p,int l,int r,int ql,int qr)
{
    if(ql==l&&qr==r)
        return tree[id][p];
    pushdown(id,p,l,r);
    int mid=(l+r)/2;
    if(qr<=mid)
        return query(id,p<<1,l,mid,ql,qr);
    else if(ql>mid)
        return query(id,p<<1|1,mid+1,r,ql,qr);
    else return min(query(id,p<<1,l,mid,ql,mid),query(id,p<<1|1,mid+1,r,mid+1,qr));
}
int main()
{
    int n,k,mn;
    scanf("%d%d",&n,&k);
    for(int i=1;i<=n;i++)
        scanf("%d",&a[i]);
    for(int i=0;i<=n;i++)
        for(int j=0;j<=k;j++)
            dp[i][j]=0x3f3f3f3f;
    dp[0][0]=0;
    for(int i=0;i<k;i++)
        build(i,1,1,n);
    for(int i=1;i<=n;i++)
    {
        for(int j=0;j<=k-1;j++)
        {
            update(j,1,1,n,1,i,i-last[a[i]]);
            update(j,1,1,n,last[a[i]]+1,i,last[a[i]]-i);
            dp[i][j+1]=query(j,1,1,n,1,i);
            if(j+1<=k-1&&i+1<=n)
            {
                update(j+1,1,1,n,i+1,i+1,-0x3f3f3f3f);
                update(j+1,1,1,n,i+1,i+1,dp[i][j+1]);
            }
        }
        last[a[i]]=i;
    }
    printf("%d\n",dp[n][k]);
    return 0;
}
### Prompt

Please create a solution in cpp to the following 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.

### Response

```cpp
#include <cstdio>
#include <algorithm>
using namespace std;
int a[35005],last[35005];
int dp[35005][105];
int tree[105][140005],lazy[105][140005];
void build(int id,int p,int l,int r)
{
    if(l==r)
    {
        tree[id][p]=dp[l-1][id];
        return;
    }
    int mid=(l+r)/2;
    build(id,p<<1,l,mid);
    build(id,p<<1|1,mid+1,r);
    tree[id][p]=min(tree[id][p<<1],tree[id][p<<1|1]);
}
void pushdown(int id,int p,int l,int r)
{
    if(lazy[id][p])
    {
        tree[id][p<<1]+=lazy[id][p];
        tree[id][p<<1|1]+=lazy[id][p];
        lazy[id][p<<1]+=lazy[id][p];
        lazy[id][p<<1|1]+=lazy[id][p];
        lazy[id][p]=0;
    }
}
void update(int id,int p,int l,int r,int ql,int qr,int d)
{
    if(ql==l&&qr==r)
    {
        tree[id][p]+=d;
        lazy[id][p]+=d;
        return;
    }
    pushdown(id,p,l,r);
    int mid=(l+r)/2;
    if(qr<=mid)
        update(id,p<<1,l,mid,ql,qr,d);
    else if(ql>mid)
        update(id,p<<1|1,mid+1,r,ql,qr,d);
    else
    {
        update(id,p<<1,l,mid,ql,mid,d);
        update(id,p<<1|1,mid+1,r,mid+1,qr,d);
    }
    tree[id][p]=min(tree[id][p<<1],tree[id][p<<1|1]);
}
int query(int id,int p,int l,int r,int ql,int qr)
{
    if(ql==l&&qr==r)
        return tree[id][p];
    pushdown(id,p,l,r);
    int mid=(l+r)/2;
    if(qr<=mid)
        return query(id,p<<1,l,mid,ql,qr);
    else if(ql>mid)
        return query(id,p<<1|1,mid+1,r,ql,qr);
    else return min(query(id,p<<1,l,mid,ql,mid),query(id,p<<1|1,mid+1,r,mid+1,qr));
}
int main()
{
    int n,k,mn;
    scanf("%d%d",&n,&k);
    for(int i=1;i<=n;i++)
        scanf("%d",&a[i]);
    for(int i=0;i<=n;i++)
        for(int j=0;j<=k;j++)
            dp[i][j]=0x3f3f3f3f;
    dp[0][0]=0;
    for(int i=0;i<k;i++)
        build(i,1,1,n);
    for(int i=1;i<=n;i++)
    {
        for(int j=0;j<=k-1;j++)
        {
            update(j,1,1,n,1,i,i-last[a[i]]);
            update(j,1,1,n,last[a[i]]+1,i,last[a[i]]-i);
            dp[i][j+1]=query(j,1,1,n,1,i);
            if(j+1<=k-1&&i+1<=n)
            {
                update(j+1,1,1,n,i+1,i+1,-0x3f3f3f3f);
                update(j+1,1,1,n,i+1,i+1,dp[i][j+1]);
            }
        }
        last[a[i]]=i;
    }
    printf("%d\n",dp[n][k]);
    return 0;
}
```