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;

typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<double, double> pdd;
typedef pair<ll, ll> pll;

#define endl "\n"
#define INF 0x3f3f3f3f
#define eb emplace_back
#define mem(a, b) memset(a , b , sizeof(a))

// const ll mod = 998244353;
const ll mod = 1e9 + 7;
const double eps = 1e-6;
const double PI = acos(-1);
const double R = 0.57721566490153286060651209;

const int N = 3e5 + 10;

#define lc u << 1
#define rc u << 1 | 1
#define mid (t[u].l + t[u].r) / 2

struct Tree {
    int l, r;
    int mn, tag;
}t[N << 1];

vector<vector<int>> dp(N, vector<int>(110));

inline void push_up(int u) {
    t[u].mn = min(t[lc].mn, t[rc].mn);
}

inline void push_down(int u) {
    if(!t[u].tag) return ;
    t[lc].tag += t[u].tag;
    t[rc].tag += t[u].tag;
    t[lc].mn  += t[u].tag;
    t[rc].mn  += t[u].tag;
    t[u].tag = 0;
}

void build(int u, int l, int r, int k) {
    t[u].l = l; t[u].r = r;
    t[u].mn = INF; t[u].tag = 0;
    if(l == r) {
        t[u].mn = dp[l][k];
        return ;
    }
    int m = l + r >> 1;
    build(lc, l, m, k);
    build(rc, m + 1, r, k);
    push_up(u);
}

void modify(int u, int ql, int qr, int val) {
    if(ql <= t[u].l && t[u].r <= qr) {
        t[u].mn += val;
        t[u].tag += val;
        return ;
    }
    push_down(u);
    if(ql <= mid) modify(lc, ql, qr, val);
    if(qr  > mid) modify(rc, ql, qr, val);
    push_up(u);
}

int query(int u, int ql, int qr) {
    if(ql <= t[u].l && t[u].r <= qr) return t[u].mn;
    push_down(u);
    int ans = INF;
    if(ql <= mid) ans = min(ans, query(lc, ql, qr));
    if(qr  > mid) ans = min(ans, query(rc, ql, qr));
    return ans;
}

void solve() {
    int n, k; cin >> n >> k;
    vector<int> a(n + 1);
    for(int i = 1;i <= n; i++) cin >> a[i];
    vector<int> pre(n + 1, -1), from(n + 1);
     
    for(int i = 1;i <= n; i++) {
        dp[i][1] = dp[i - 1][1];
        from[i] = pre[a[i]];
        if(from[i] != -1) dp[i][1] += i - from[i];
        pre[a[i]] = i;
    }
    for(int i = 2;i <= k; i++) {
        build(1, 1, n, i - 1);
        for(int j = i;j <= n; j++) {
            if(from[j] != -1) modify(1, 1, from[j] - 1, j - from[j]);
            dp[j][i] = min(dp[j - 1][i - 1], query(1, i - 1, j - 1));
        }
    }
    cout << dp[n][k] << endl;
}

signed main() {
    ios_base::sync_with_stdio(false);
    // cin.tie(nullptr);
    // cout.tie(nullptr);
#ifdef FZT_ACM_LOCAL
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);
    signed test_index_for_debug = 1;
    char acm_local_for_debug = 0;
    do {
        if (acm_local_for_debug == '$') exit(0);
        if (test_index_for_debug > 20)
            throw runtime_error("Check the stdin!!!");
        auto start_clock_for_debug = clock();
        solve();
        auto end_clock_for_debug = clock();
        cout << "Test " << test_index_for_debug << " successful" << endl;
        cerr << "Test " << test_index_for_debug++ << " Run Time: "
             << double(end_clock_for_debug - start_clock_for_debug) / CLOCKS_PER_SEC << "s" << endl;
        cout << "--------------------------------------------------" << endl;
    } while (cin >> acm_local_for_debug && cin.putback(acm_local_for_debug));
#else
    solve();
#endif
    return 0;
}