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:
import java.util.*;
import java.io.*;

public class Main {
	static long mod = 1000000007;
	static int INF = 1000000000;
 	public static void main(String[] args){
		FastScanner scanner = new FastScanner();
		int n = scanner.nextInt();
		int m = scanner.nextInt();
		String s = scanner.next();
		int[][] cnt = new int[20][20];
		for(int i = 0; i < n-1; i++){
			cnt[s.charAt(i)-'a'][s.charAt(i+1)-'a']++;
			cnt[s.charAt(i+1)-'a'][s.charAt(i)-'a']++;
		}
		//dp[i]:= 文字列i(この中に同一文字は含まれない)を作った時のコストの最小値
		int[] dp = new int[(1<<m)];
		for(int i = 0; i < (1<<m); i++){
			dp[i] = INF;
		}
		dp[0] = 0;
		for(int i = 0; i < (1<<m); i++){
			int cost = 0;
			for(int j = 0; j < m; j++){
				if((i>>j & 1) == 0){
					for(int k = 0; k < m; k++){
						if((~i>>k & 1) == 0){
							cost += cnt[j][k];
						}
					}
				}
			}
			for(int j = 0; j < m; j++){
				dp[i|1<<j] = Math.min(dp[i|1<<j],dp[i]+cost);
			}
		}
		System.out.println(dp[(1<<m)-1]);
	}
	static class BIT{
		int n;
		int[] bit;
		public BIT(int n){
			this.n = n;
			bit = new int[n+1];
		}
		void add(int idx, int val){
			for(int i = idx+1; i <= n; i += i&(-i)) bit[i-1] += val;
		}
		int sum(int idx){
			int res = 0;
			for(int i = idx+1; i > 0; i -= i&(-i)) res += bit[i-1];
			return res;
		}
		int sum(int begin, int end){
			if(begin == 0) return sum(end);
			return sum(end)-sum(begin-1);
		}
	}
	static class Pair implements Comparable<Pair>{
    int first, second;
    Pair(int a, int b){
        first = a;
        second = b;
    }
    @Override
    public boolean equals(Object o){
        if (this == o) return true;
        if (!(o instanceof Pair)) return false;
        Pair p = (Pair) o;
        return first == p.first && second == p.second;
    }
    @Override
    public int compareTo(Pair p){
        return first == p.first ? second - p.second : first - p.first; //firstで昇順にソート
        //return (first == p.first ? second - p.second : first - p.first) * -1; //firstで降順にソート
        //return second == p.second ? first - p.first : second - p.second;//secondで昇順にソート
        //return (second == p.second ? first - p.first : second - p.second)*-1;//secondで降順にソート
		    //return first * 1.0 / second > p.first * 1.0 / p.second ? 1 : -1; // first/secondの昇順にソート
		    //return first * 1.0 / second < p.first * 1.0 / p.second ? 1 : -1; // first/secondの降順にソート
				//return second * 1.0 / first > p.second * 1.0 / p.first ? 1 : -1; // second/firstの昇順にソート
		    //return second * 1.0 / first < p.second * 1.0 / p.first ? 1 : -1; // second/firstの降順にソート
				//return Math.atan2(second, first) > Math.atan2(p.second, p.first) ? 1 : -1; // second/firstの昇順にソート
				//return first + second > p.first + p.second ? 1 : -1; //first+secondの昇順にソート
				//return first + second < p.first + p.second ? 1 : -1; //first+secondの降順にソート
				//return first - second < p.first - p.second ? 1 : -1; //first-secondの降順にソート
		}
  }

	private static class FastScanner {
		private final InputStream in = System.in;
		private final byte[] buffer = new byte[1024];
		private int ptr = 0;
		private int buflen = 0;
		private boolean hasNextByte() {
				if (ptr < buflen) {
						return true;
				}else{
						ptr = 0;
						try {
								buflen = in.read(buffer);
						} catch (IOException e) {
								e.printStackTrace();
						}
						if (buflen <= 0) {
								return false;
						}
				}
				return true;
		}
		private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
		private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
		public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
		public String next() {
				if (!hasNext()) throw new NoSuchElementException();
				StringBuilder sb = new StringBuilder();
				int b = readByte();
				while(isPrintableChar(b)) {
						sb.appendCodePoint(b);
						b = readByte();
				}
				return sb.toString();
		}
		public long nextLong() {
				if (!hasNext()) throw new NoSuchElementException();
				long n = 0;
				boolean minus = false;
				int b = readByte();
				if (b == '-') {
						minus = true;
						b = readByte();
				}
				if (b < '0' || '9' < b) {
						throw new NumberFormatException();
				}
				while(true){
						if ('0' <= b && b <= '9') {
								n *= 10;
								n += b - '0';
						}else if(b == -1 || !isPrintableChar(b)){
								return minus ? -n : n;
						}else{
								throw new NumberFormatException();
						}
						b = readByte();
				}
		}
		public int nextInt() {
				long nl = nextLong();
				if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
				return (int) nl;
		}
		public double nextDouble() { return Double.parseDouble(next());}
	}
}