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:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.io.IOException;
import java.util.stream.Collectors;
import java.io.UncheckedIOException;
import java.util.List;
import java.util.stream.Stream;
import java.util.Map;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            BGameWithString solver = new BGameWithString();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class BGameWithString {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            char[] s = in.readString().toCharArray();
            int n = s.length;
            Rotate[] rotates = new Rotate[n];
            for (int i = 0; i < n; i++) {
                rotates[i] = new Rotate(s, i);
            }
            Map<Integer, List<Rotate>> groupByFirst =
                    Stream.of(rotates)
                            .collect(Collectors.groupingBy(x -> x.get(0)));

            Rotate[] appear = new Rotate['z' - 'a' + 1];
            long sum = 0;
            Rotate dump = new Rotate(s, 0);
            for (List<Rotate> list : groupByFirst.values()) {
//            for (Rotate r : list) {
//                System.err.println(r);
//            }
                long max = 0;
                for (int i = 0; i < n; i++) {
                    Arrays.fill(appear, null);
                    for (Rotate r : list) {
                        int c = r.get(i) - 'a';
                        if (appear[c] != null) {
                            appear[c] = dump;
                        } else {
                            appear[c] = r;
                        }
                    }
                    int cnt = 0;
                    for (Rotate r : appear) {
                        if (r != null && r != dump) {
                            cnt++;
                        }
                    }
                    max = Math.max(max, cnt);
                }

                sum += max;
            }

            out.printf("%.15f", (double) sum / n);
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput printf(String format, Object... args) {
            cache.append(String.format(format, args));
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class Rotate {
        char[] s;
        int begin;

        public Rotate(char[] s, int begin) {
            this.s = s;
            this.begin = begin;
        }

        public int get(int i) {
            i += begin;
            if (i >= s.length) {
                i -= s.length;
            }
            return s[i];
        }

        public String toString() {
            int n = s.length;
            StringBuilder builder = new StringBuilder(n);
            for (int i = 0; i < n; i++) {
                builder.append((char) get(i));
            }
            return builder.toString();
        }

    }

    static class FastInput {
        private final InputStream is;
        private StringBuilder defaultStringBuf = new StringBuilder(1 << 13);
        private byte[] buf = new byte[1 << 20];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public String readString(StringBuilder builder) {
            skipBlank();

            while (next > 32) {
                builder.append((char) next);
                next = read();
            }

            return builder.toString();
        }

        public String readString() {
            defaultStringBuf.setLength(0);
            return readString(defaultStringBuf);
        }

    }
}