Problem: Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose.

Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability. 

Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win.

Input

The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only.

Output

Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>

Examples

Input

technocup


Output

1.000000000000000


Input

tictictactac


Output

0.333333333333333


Input

bbaabaabbb


Output

0.100000000000000

Note

In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely.

In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely.

Solution (in JAVA):

Solution:
// package cf931;

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.math.BigInteger;
import java.util.*;
import java.util.function.Supplier;
import java.util.stream.IntStream;

import static java.util.Arrays.stream;
import static java.util.stream.Collectors.toMap;

public class CFD { //E
    private static final String INPUT = "bbaabaabbb\n";

    FastScanner sc;

    public static void main(String[] args) {
        new CFD().run();
    }

    public void run() {
        sc = new FastScanner(oj ? System.in : new ByteArrayInputStream(INPUT.getBytes()));

        long s = System.currentTimeMillis();
        solve();
        System.out.flush();
        tr(System.currentTimeMillis() - s + "ms");
    }

    public void solve() {
        char[] chars = sc.nextLine().toCharArray();
        int n = chars.length;

        Map<Character, List<Integer>> places = new TreeMap<>();
        for (int i = 0; i < n; i++) {
            places.computeIfAbsent(chars[i], ch -> new ArrayList<>()).add(i);
        }

        int res = 0;
        int[] chart = new int[26];
        for (Map.Entry<Character, List<Integer>> entry : places.entrySet()) {
            int chance = 0;
            for (int i = 1; i < n; i++) { //shift
                Arrays.fill(chart, 0);
                int curChance = 0;
                for (int pos : entry.getValue()) {
                    int count = ++chart[chars[(pos + i) % n] - 'a'];
                    if (count == 1) curChance++;
                    if (count == 2) curChance--;
                }
                if (curChance == entry.getValue().size()) {
                    chance = curChance;
                    break;
                } else {
                    chance = Math.max(curChance, chance);
                }
            }
            res += chance;
        }
        System.out.println((double)res / n);
    }

    //********************************************************************************************
    //********************************************************************************************
    //********************************************************************************************

    private static int ceil(double d) {
        int ret = (int) d;
        return ret == d ? ret : ret + 1;
    }

    private static int round(double d) {
        return (int) (d + 0.5);
    }

    private static <T> T elvis(T obj, Supplier<T> defValue) {
        return obj == null ? defValue.get() : obj;
    }

    @SuppressWarnings("SameParameterValue")
    private static <T> T elvis(T obj, T defValue) {
        return obj == null ? defValue : obj;
    }

    private static int gcd(int a, int b) {
        BigInteger b1 = BigInteger.valueOf(a);
        BigInteger b2 = BigInteger.valueOf(b);
        BigInteger gcd = b1.gcd(b2);
        return gcd.intValue();
    }

    private static long gcd(long a, long b) {
        BigInteger b1 = BigInteger.valueOf(a);
        BigInteger b2 = BigInteger.valueOf(b);
        BigInteger gcd = b1.gcd(b2);
        return gcd.longValue();
    }

    private int[] readIntArray(int n) {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = sc.nextInt();
        }
        return res;
    }

    private long[] readLongArray(int n) {
        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[i] = sc.nextLong();
        }
        return res;
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        FastScanner(InputStream stream) {
            this.stream = stream;
        }

        int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) return -1;
            }
            return buf[curChar++];
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        boolean isEndline(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String next() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = read();
            while (isEndline(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndline(c));
            return res.toString();
        }
    }

    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;

    private void tr(Object... o) {
        if (!oj) System.out.println(Arrays.deepToString(o));
    }
}