Problem: You have a password which you often type — a string s of length n. Every character of this string is one of the first m lowercase Latin letters.

Since you spend a lot of time typing it, you want to buy a new keyboard.

A keyboard is a permutation of the first m Latin letters. For example, if m = 3, then there are six possible keyboards: abc, acb, bac, bca, cab and cba.

Since you type your password with one finger, you need to spend time moving your finger from one password character to the next. The time to move from character s_i to character s_{i+1} is equal to the distance between these characters on keyboard. The total time you have to spend typing the password with a keyboard is called the slowness of this keyboard.

More formaly, the slowness of keyboard is equal to ∑_{i=2}^{n} |pos_{s_{i-1}} - pos_{s_i} |, where pos_x is position of letter x in keyboard.

For example, if s is aacabc and the keyboard is bac, then the total time of typing this password is |pos_a - pos_a| + |pos_a - pos_c| + |pos_c - pos_a| + |pos_a - pos_b| + |pos_b - pos_c| = |2 - 2| + |2 - 3| + |3 - 2| + |2 - 1| + |1 - 3| = 0 + 1 + 1 + 1 + 2 = 5.

Before buying a new keyboard you want to know the minimum possible slowness that the keyboard can have. 

Input

The first line contains two integers n and m (1 ≤ n ≤ 10^5, 1 ≤ m ≤ 20).

The second line contains the string s consisting of n characters. Each character is one of the first m Latin letters (lowercase).

Output

Print one integer – the minimum slowness a keyboard can have.

Examples

Input


6 3
aacabc


Output


5


Input


6 4
aaaaaa


Output


0


Input


15 4
abacabadabacaba


Output


16

Note

The first test case is considered in the statement.

In the second test case the slowness of any keyboard is 0.

In the third test case one of the most suitable keyboards is bacd.

Solution (in JAVA):

Solution:
/*Author: Satyajeet Singh, Delhi Technological University*/
    import java.io.*;
    import java.util.*;
    import java.text.*; 
    import java.lang.*;
    import java.math.*;
 
public class Main{
/*********************************************Constants******************************************/
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));        
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static long mod=(long)1e9+7;
    static long mod1=998244353;
    static boolean sieve[];
    static ArrayList<Integer> primes;
    static long factorial[],invFactorial[];
    static ArrayList<Pair> graph[];
    static boolean oj = System.getProperty("ONLINE_JUDGE") != null;
/****************************************Solutions Begins***************************************/  
    static int n,m;
    static long cost[][],dp[];
    public static void main(String[] args) throws Exception{
        String st[]=nl();
        n=pi(st[0]);
        m=pi(st[1]);
        st=nl();
        String str=st[0];
        int mn=10000;
        for(int i=0;i<n;i++){
            mn=Math.min(mn,str.charAt(i));
        }
        cost=new long[m][m];
        for(int i=1;i<n;i++){
            int a1=str.charAt(i-1)-mn;
            int a2=str.charAt(i)-mn;
            if(a1==a2)continue;
            cost[a1][a2]++;
            cost[a2][a1]++;
        }
        int mm=1<<m;
        dp=new long[mm];
        Arrays.fill(dp,Long.MAX_VALUE/2);
        dp[0]=0;
        //debug(cost);
        long cntbit[]=new long[mm];
        int minbit[]=new int[mm];

        for(int mask=1;mask<mm;mask++){
            cntbit[mask]=1+cntbit[(mask&(mask-1))];
            for(int i=0;i<m;i++){
                if(((mask>>i)&1)!=0){
                    minbit[mask]=i;
                    break;
                }
            }
        }
        long cntcost[][]=new long[mm][m];
        for(int mask=0;mask<mm;mask++){
            for(int i=0;i<m;i++){
                int b=minbit[mask];
                cntcost[mask][i]=cntcost[mask^(1<<b)][i]+cost[i][b];
            }
        }
        int yy=mm-1;
        for(int mask=0;mask<mm;mask++){
            long cnt=cntbit[mask];
            for(int i=0;i<m;i++){
                if(((mask>>i)&1)!=0){
                    long ans=cnt*(cntcost[mask][i]-cntcost[yy^mask][i]);
                    dp[mask]=Math.min(dp[mask],dp[mask^(1<<i)]+ans);
                }
            }
        }
        out.println(dp[mm-1]);
/****************************************Solutions Ends**************************************************/
        out.flush();
        out.close();
    }
/****************************************Template Begins************************************************/
    static String[] nl() throws Exception{
        return br.readLine().split(" ");
    }
    static String[] nls() throws Exception{
        return br.readLine().split("");
    }
    static int pi(String str) {
        return Integer.parseInt(str);
    }
    static long pl(String str){
        return Long.parseLong(str);
    }
    static double pd(String str){
        return Double.parseDouble(str);
    }
/***************************************Precision Printing**********************************************/
    static void printPrecision(double d){
        DecimalFormat ft = new DecimalFormat("0.000000000000000000000"); 
        out.println(ft.format(d));
    }
/**************************************Bit Manipulation**************************************************/
    static void printMask(long mask){
        System.out.println(Long.toBinaryString(mask));
    }
    static int countBit(long mask){
        int ans=0;
        while(mask!=0){
            if(mask%2==1){
                ans++;
            }
            mask/=2;
        }
        return ans;
    }
/******************************************Graph*********************************************************/
    static void Makegraph(int n){
        graph=new ArrayList[n];
        for(int i=0;i<n;i++){
            graph[i]=new ArrayList<>();
        }
    }
    static void addEdge(int a,int b){
        graph[a].add(new Pair(b,1));
    }
    static void addEdge(int a,int b,int c){
        graph[a].add(new Pair(b,c));
    }    
/*********************************************PAIR********************************************************/
    static class PairComp implements Comparator<Pair>{
        public int compare(Pair p1,Pair p2){
            return p1.u-p2.u;
        }
    }
    static class Pair implements Comparable<Pair> {
        int u;
        int v;
        int index=-1;
        public Pair(int u, int v) {
            this.u = u;
            this.v = v;
        }
        public int hashCode() {
            int hu = (int) (u ^ (u >>> 32));
            int hv = (int) (v ^ (v >>> 32));
            return 31 * hu + hv;
        }
        public boolean equals(Object o) {
            Pair other = (Pair) o;
            return u == other.u && v == other.v;
        }
        public int compareTo(Pair other) {
            if(index!=other.index)
                return Long.compare(index, other.index);
            return Long.compare(v, other.v)!=0?Long.compare(v, other.v):Long.compare(u, other.u);
        }
        public String toString() {
            return "[u=" + u + ", v=" + v + "]";
        }
    }
/******************************************Long Pair*******************************************************/
    static class PairCompL implements Comparator<Pairl>{
        public int compare(Pairl p1,Pairl p2){
            long a=p1.u*p2.v;
            long b=p2.u*p1.v;
            if(a>b){
                return -1;
            }
            else if(a<b){
                return 1;
            }
            else{
                return 0;
            }
        }
    }
    static class Pairl implements Comparable<Pairl> {
            long u;
            long v;
            int index=-1;
            public Pairl(long u, long v) {
                this.u = u;
                this.v = v;
            }
    
            public int hashCode() {
                int hu = (int) (u ^ (u >>> 32));
                int hv = (int) (v ^ (v >>> 32));
                return 31 * hu + hv;
            }
    
            public boolean equals(Object o) {
                Pairl other = (Pairl) o;
                return u == other.u && v == other.v;
            }
    
            public int compareTo(Pairl other) {
                if(index!=other.index)
                    return Long.compare(index, other.index);
                return Long.compare(v, other.v)!=0?Long.compare(v, other.v):Long.compare(u, other.u);
            }
    
            public String toString() {
                return "[u=" + u + ", v=" + v + "]";
            }
        }
/*****************************************DEBUG***********************************************************/
    public static void debug(Object... o) {
        if(!oj)
        System.out.println(Arrays.deepToString(o));
    }
/************************************MODULAR EXPONENTIATION***********************************************/
    static long modulo(long a,long b,long c) {
        long x=1;
        long y=a%c;
        while(b > 0){
            if(b%2 == 1){
                x=(x*y)%c;
            }
            y = (y*y)%c; // squaring the base
            b /= 2;
        }
        return  x%c;
    }
/********************************************GCD**********************************************************/
    static long gcd(long x, long y)
    {
        if(x==0)
            return y;
        if(y==0)
            return x;
        long r=0, a, b;
        a = (x > y) ? x : y; // a is greater number
        b = (x < y) ? x : y; // b is smaller number
        r = b;
        while(a % b != 0)
        {
            r = a % b;
            a = b;
            b = r;
        }
        return r;
    }
/******************************************SIEVE**********************************************************/
    static void sieveMake(int n){
        sieve=new boolean[n];
        Arrays.fill(sieve,true);
        sieve[0]=false;
        sieve[1]=false;
        for(int i=2;i*i<n;i++){
            if(sieve[i]){
                for(int j=i*i;j<n;j+=i){
                    sieve[j]=false;
                }
            }
        }
        primes=new ArrayList<Integer>();
        for(int i=0;i<n;i++){
            if(sieve[i]){
                primes.add(i);
            }
        }        
    }
/********************************************End***********************************************************/
}