Problem:
Score : 1400 points

Problem Statement

Consider the following set of rules for encoding strings consisting of 0 and 1:

Strings 0 and 1 can be encoded as 0 and 1, respectively.

If strings A and B can be encoded as P and Q, respectively, then string AB can be encoded as PQ.

If string A can be encoded as P and K \geq 2 is a positive integer, then string AA...A (A repeated K times) can be encoded as (PxK).

For example, string 001001001, among other possibilities, can be encoded as 001001001, 00(1(0x2)x2)1 and (001x3).

Let's call string A a subset of string B if:

A and B are equal in length and consist of 0 and 1;

for all indices i such that A_i = 1, it's also true that B_i = 1.

You are given string S consisting of 0 and 1. Find the total number of distinct encodings of all subsets of S, modulo 998244353.

Constraints

1 \leq |S| \leq 100

S consists of 0 and 1.

Input

Input is given from Standard Input in the following format:

S

Output

Print the total number of distinct encodings of all subsets of S modulo 998244353.

Sample Input 1

011

Sample Output 1

9

There are four subsets of S:

011 can be encoded as 011 and 0(1x2);

010 can be encoded as 010;

001 can be encoded as 001 and (0x2)1;

000 can be encoded as 000, 0(0x2), (0x2)0 and (0x3).

Thus, the total number of encodings of all subsets of S is 2 + 1 + 2 + 4 = 9.

Sample Input 2

0000

Sample Output 2

10

This time S has only one subset, but it can be encoded in 10 different ways.

Sample Input 3

101110

Sample Output 3

156

Sample Input 4

001110111010110001100000100111

Sample Output 4

363383189

Don't forget to take the result modulo 998244353.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.IOException;
import java.io.Serializable;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
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);
            EEncodingSubsets solver = new EEncodingSubsets();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class EEncodingSubsets {
        Modular mod = new Modular(998244353);
        Map<BitSet, Integer> dp = new HashMap<>((int) 1e6);

        public void solve(int testNumber, FastInput in, FastOutput out) {
            char[] s = in.readString().toCharArray();
            int n = s.length;
            BitSet bs = new BitSet(n);
            for (int i = 0; i < n; i++) {
                if (s[i] == '1') {
                    bs.set(i);
                }
            }

            int ans = dp(bs);
            out.println(ans);
        }

        public int dp(BitSet bs) {
            Integer ans = dp.get(bs);
            if (ans == null) {
                if (bs.capacity() == 0) {
                    ans = 1;
                    dp.put(bs, ans);
                    return ans;
                }

                int normal = dp(bs.interval(1, bs.capacity() - 1));
                if (bs.get(0)) {
                    normal = mod.mul(normal, 2);
                }

                int special = 0;
                for (int i = 1; i <= bs.capacity() / 2; i++) {
                    for (int k = 2; k * i <= bs.capacity(); k++) {
                        BitSet state = new BitSet(i);
                        state.fill(true);
                        for (int j = 0; j < k * i; j += i) {
                            state.and(bs.interval(j, j + i - 1));
                        }
                        special = mod.plus(special, mod.mul(dp(state), dp(bs.interval(k * i, bs.capacity() - 1))));
                    }
                }

                ans = mod.plus(normal, special);
                dp.put(bs, ans);
            }

            return ans;
        }

    }

    static class Modular {
        int m;

        public Modular(int m) {
            this.m = m;
        }

        public Modular(long m) {
            this.m = (int) m;
            if (this.m != m) {
                throw new IllegalArgumentException();
            }
        }

        public Modular(double m) {
            this.m = (int) m;
            if (this.m != m) {
                throw new IllegalArgumentException();
            }
        }

        public int valueOf(int x) {
            x %= m;
            if (x < 0) {
                x += m;
            }
            return x;
        }

        public int valueOf(long x) {
            x %= m;
            if (x < 0) {
                x += m;
            }
            return (int) x;
        }

        public int mul(int x, int y) {
            return valueOf((long) x * y);
        }

        public int plus(int x, int y) {
            return valueOf(x + y);
        }

        public String toString() {
            return "mod " + m;
        }

    }

    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 append(int c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(int c) {
            return append(c).println();
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            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 FastInput {
        private final InputStream is;
        private StringBuilder defaultStringBuf = new StringBuilder(1 << 13);
        private byte[] buf = new byte[1 << 13];
        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);
        }

    }

    static final class BitSet implements Serializable, Cloneable {
        private long[] data;
        private long tailAvailable;
        private int totalBit;
        private int m;
        private static final int SHIFT = 6;
        private static final int LOW = 63;
        private static final int BITS_FOR_EACH = 64;
        private static final long ALL_ONE = ~0L;
        private static final long ALL_ZERO = 0L;
        private static final BitSet EMPTY = new BitSet(0);

        public BitSet(int n) {
            totalBit = n;
            this.m = (totalBit + 64 - 1) / 64;
            data = new long[m];
            tailAvailable = oneBetween(0, offset(totalBit - 1));
        }

        public BitSet(BitSet bs) {
            this.data = bs.data.clone();
            this.tailAvailable = bs.tailAvailable;
            this.totalBit = bs.totalBit;
            this.m = bs.m;
        }

        public BitSet interval(int l, int r) {
            if (r < l) {
                return EMPTY;
            }
            return new BitSet(this, l, r);
        }

        private BitSet(BitSet bs, int l, int r) {
            totalBit = r - l + 1;
            tailAvailable = oneBetween(0, offset(totalBit - 1));
            data = Arrays.copyOfRange(bs.data, word(l), word(r) + 1);
            this.m = data.length;
            leftShift(offset(l));
            this.m = (totalBit + 64 - 1) / 64;
            data[m - 1] &= tailAvailable;
            for (int i = m; i < data.length; i++) {
                data[i] = 0;
            }
        }

        public boolean get(int i) {
            return (data[word(i)] & (1L << offset(i))) != 0;
        }

        public void set(int i) {
            data[word(i)] |= (1L << offset(i));
        }

        private static int word(int i) {
            return i >>> SHIFT;
        }

        private static int offset(int i) {
            return i & LOW;
        }

        private long oneBetween(int l, int r) {
            if (r < l) {
                return 0;
            }
            long lBegin = 1L << offset(l);
            long rEnd = 1L << offset(r);
            return (ALL_ONE ^ (lBegin - 1)) & ((rEnd << 1) - 1);
        }

        public void fill(boolean val) {
            if (val) {
                set(0, capacity() - 1);
            } else {
                clear(0, capacity() - 1);
            }
        }

        public void set(int l, int r) {
            if (r < l) {
                return;
            }
            int lWord = l >>> SHIFT;
            int rWord = r >>> SHIFT;
            for (int i = lWord + 1; i < rWord; i++) {
                data[i] = ALL_ONE;
            }
            //lword
            if (lWord == rWord) {
                data[lWord] |= oneBetween(offset(l), offset(r));
            } else {
                data[lWord] |= oneBetween(offset(l), 63);
                data[rWord] |= oneBetween(0, offset(r));
            }
        }

        public void clear(int l, int r) {
            if (r < l) {
                return;
            }
            int lWord = l >>> SHIFT;
            int rWord = r >>> SHIFT;
            for (int i = lWord + 1; i < rWord; i++) {
                data[i] = ALL_ZERO;
            }
            //lword
            if (lWord == rWord) {
                data[lWord] &= ~oneBetween(offset(l), offset(r));
            } else {
                data[lWord] &= ~oneBetween(offset(l), 63);
                data[rWord] &= ~oneBetween(0, offset(r));
            }
        }

        public int capacity() {
            return totalBit;
        }

        public void and(BitSet bs) {
            int n = Math.min(this.m, bs.m);
            for (int i = 0; i < n; i++) {
                data[i] &= bs.data[i];
            }
        }

        public int nextSetBit(int start) {
            int offset = offset(start);
            int w = word(start);
            if (offset != 0) {
                long mask = oneBetween(offset, 63);
                if ((data[w] & mask) != 0) {
                    return Long.numberOfTrailingZeros(data[w] & mask) + w * BITS_FOR_EACH;
                }
                w++;
            }

            while (w < m && data[w] == ALL_ZERO) {
                w++;
            }
            if (w >= m) {
                return capacity();
            }
            return Long.numberOfTrailingZeros(data[w]) + w * BITS_FOR_EACH;
        }

        public void leftShift(int n) {
            int wordMove = word(n);
            int offsetMove = offset(n);
            int rshift = 63 - (offsetMove - 1);

            if (offsetMove != 0) {
                //slightly
                for (int i = 0; i < m; i++) {
                    if (i > 0) {
                        data[i - 1] |= data[i] << rshift;
                    }
                    data[i] >>>= offsetMove;
                }
            }
            if (wordMove > 0) {
                for (int i = 0; i < m; i++) {
                    if (i >= wordMove) {
                        data[i - wordMove] = data[i];
                    }
                    data[i] = 0;
                }
            }
        }

        public BitSet clone() {
            return new BitSet(this);
        }

        public String toString() {
            StringBuilder builder = new StringBuilder("{");
            for (int i = nextSetBit(0); i < capacity(); i++) {
                builder.append(i).append(',');
            }
            if (builder.length() > 1) {
                builder.setLength(builder.length() - 1);
            }
            builder.append("}");
            return builder.toString();
        }

        public int hashCode() {
            long ans = 1;
            for (int i = 0; i < m; i++) {
                ans = ans * 31 + data[i];
            }
            return (int) ans;
        }

        public boolean equals(Object obj) {
            if (!(obj instanceof BitSet)) {
                return false;
            }
            BitSet other = (BitSet) obj;
            if (other.totalBit != totalBit) {
                return false;
            }
            for (int i = 0; i < m; i++) {
                if (other.data[i] != data[i]) {
                    return false;
                }
            }
            return true;
        }

    }
}