Problem: You are given a string s consisting of characters "1", "0", and "?". The first character of s is guaranteed to be "1". Let m be the number of characters in s.

Count the number of ways we can choose a pair of integers a, b that satisfies the following: 

  * 1 ≤ a < b < 2^m 
  * When written without leading zeros, the base-2 representations of a and b are both palindromes. 
  * The base-2 representation of bitwise XOR of a and b matches the pattern s. We say that t matches s if the lengths of t and s are the same and for every i, the i-th character of t is equal to the i-th character of s, or the i-th character of s is "?". 



Compute this count modulo 998244353. 

Input

The first line contains a single string s (1 ≤ |s| ≤ 1 000). s consists only of characters "1", "0" and "?". It is guaranteed that the first character of s is a "1".

Output

Print a single integer, the count of pairs that satisfy the conditions modulo 998244353.

Examples

Input


10110


Output


3


Input


1?0???10


Output


44


Input


1?????????????????????????????????????


Output


519569202


Input


1


Output


0

Note

For the first example, the pairs in base-2 are (111, 10001), (11, 10101), (1001, 11111).

Solution (in JAVA):

Solution:


import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.nio.charset.Charset;
import java.util.*;

public class CF1147D {
    public static void main(String[] args) throws Exception {
        boolean local = System.getProperty("ONLINE_JUDGE") == null;
        boolean async = false;

        Charset charset = Charset.forName("ascii");

        FastIO io = local ? new FastIO(new FileInputStream("D:\\DATABASE\\TESTCASE\\Code.in"), System.out, charset) : new FastIO(System.in, System.out, charset);
        Task task = new Task(io, new Debug(local));

        if (async) {
            Thread t = new Thread(null, task, "dalt", 1 << 27);
            t.setPriority(Thread.MAX_PRIORITY);
            t.start();
            t.join();
        } else {
            task.run();
        }

        if (local) {
            io.cache.append("\n\n--memory -- \n" + ((Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()) >> 20) + "M");
        }

        io.flush();
    }

    public static class Task implements Runnable {
        final FastIO io;
        final Debug debug;
        int inf = (int) 1e8;
        int mod = (int) 998244353;

        public int mod(int val) {
            val %= mod;
            if (val < 0) {
                val += mod;
            }
            return val;
        }

        public int mod(long val) {
            val %= mod;
            if (val < 0) {
                val += mod;
            }
            return (int) val;
        }

        int bitAt(int x, int i) {
            return (x >> i) & 1;
        }

        int bitAt(long x, int i) {
            return (int) ((x >> i) & 1);
        }

        public Task(FastIO io, Debug debug) {
            this.io = io;
            this.debug = debug;
        }

        @Override
        public void run() {
            solve();
        }

        String s;

        public void solve() {
            s = new StringBuilder(io.readString()).reverse().toString();
            int total = 0;
            for (int i = 1; i < s.length(); i++) {
                total = mod(total + count(i));
            }
            io.cache.append(total);
        }

        public Node[] createNodes(int n, String id) {
            Node[] nodes = new Node[n];
            for (int i = 0; i < n; i++) {
                nodes[i] = new Node();
                //nodes[i].id = id + "-" + i;
            }
            return nodes;
        }

        public int count(int m) {
            int n = s.length();
            Node[] a = createNodes(n, "a");
            Node[] b = createNodes(m, "b");
            Node alwaysTrue = new Node();

            addEdge(a[n - 1], alwaysTrue, true);
            addEdge(b[m - 1], alwaysTrue, true);

            asPalindrome(a);
            asPalindrome(b);

            for (int i = n - 1; i >= m; i--) {
                char c = s.charAt(i);
                if (c == '0') {
                    addEdge(a[i], alwaysTrue, false);
                } else if (c == '1') {
                    addEdge(a[i], alwaysTrue, true);
                }
            }

            for (int i = m - 1; i >= 0; i--) {
                char c = s.charAt(i);
                if (c == '0') {
                    addEdge(a[i], b[i], true);
                } else if (c == '1') {
                    addEdge(a[i], b[i], false);
                }
            }

            int setCount = 0;
            boolean able = ablePaint(alwaysTrue, 1);
            tarjan(alwaysTrue, null);
            if (alwaysTrue.set == alwaysTrue) {
                setCount++;
            }
            for (Node node : a) {
                if (node.color != 0) {
                    continue;
                }
                able = able && ablePaint(node, 1);
                tarjan(node, null);
                if (node.set == node) {
                    setCount++;
                }
            }
            for (Node node : b) {
                if (node.color != 0) {
                    continue;
                }
                able = able && ablePaint(node, 1);
                tarjan(node, null);
                if (node.set == node) {
                    setCount++;
                }
            }

            if (!able) {
                return 0;
            }

            return Mathematics.pow(2, setCount - 1, mod);
        }

        int order = 1;

        int order() {
            return order++;
        }

        Deque<Node> tarjanDeque = new ArrayDeque<>();

        public void tarjan(Node root, Edge from) {
            if (root.dfn != 0) {
                return;
            }
            root.dfn = root.low = order();
            tarjanDeque.addLast(root);
            root.inStack = true;
            for (Edge edge : root.edges) {
                if (edge == from) {
                    continue;
                }
                Node node = edge.another(root);
                tarjan(node, edge);
                if (node.inStack) {
                    root.low = Math.min(root.low, node.low);
                }
            }

            if (root.dfn == root.low) {
                while (true) {
                    Node tail = tarjanDeque.removeLast();
                    tail.set = root;
                    tail.inStack = false;
                    if (tail == root) {
                        break;
                    }
                }
            }
        }

        public boolean ablePaint(Node a, int color) {
            if (a.color != 0) {
                return a.color == color;
            }
            a.color = color;
            for (Edge edge : a.edges) {
                Node node = edge.another(a);
                if (!ablePaint(node, edge.sameColor ? color : -color)) {
                    return false;
                }
            }
            return true;
        }

        public void asPalindrome(Node[] nodes) {
            int l = 0;
            int r = nodes.length - 1;
            while (l < r) {
                addEdge(nodes[l], nodes[r], true);
                l++;
                r--;
            }
        }


        public void addEdge(Node a, Node b, boolean same) {
            Edge edge = new Edge(a, b, same);
            a.edges.add(edge);
            b.edges.add(edge);
        }
    }

    public static class Node {
        List<Edge> edges = new ArrayList<>();
        int color;
        int dfn;
        boolean inStack;
        int low;
        Node set;
    }

    public static class Edge {
        final Node a;
        final Node b;
        final boolean sameColor;

        public Edge(Node a, Node b, boolean sameColor) {
            this.a = a;
            this.b = b;
            this.sameColor = sameColor;
        }

        public Node another(Node me) {
            return a == me ? b : a;
        }

        @Override
        public String toString() {
            return a + "<->" + b;
        }
    }

    public static class Mathematics {

        public static int ceilPowerOf2(int x) {
            return 32 - Integer.numberOfLeadingZeros(x - 1);
        }

        public static int floorPowerOf2(int x) {
            return 31 - Integer.numberOfLeadingZeros(x);
        }

        public static long modmul(long a, long b, long mod) {
            return b == 0 ? 0 : ((modmul(a, b >> 1, mod) << 1) % mod + a * (b & 1)) % mod;
        }

        /**
         * Get the greatest common divisor of a and b
         */
        public static int gcd(int a, int b) {
            return a >= b ? gcd0(a, b) : gcd0(b, a);
        }

        private static int gcd0(int a, int b) {
            return b == 0 ? a : gcd0(b, a % b);
        }

        public static int extgcd(int a, int b, int[] coe) {
            if (a >= b) {
                return extgcd0(a, b, coe);
            } else {
                int g = extgcd0(b, a, coe);
                int tmp = coe[0];
                coe[0] = coe[1];
                coe[1] = tmp;
                return g;
            }
        }

        private static int extgcd0(int a, int b, int[] coe) {
            if (b == 0) {
                coe[0] = 1;
                coe[1] = 0;
                return a;
            }
            int g = extgcd0(b, a % b, coe);
            int n = coe[0];
            int m = coe[1];
            coe[0] = m;
            coe[1] = n - m * (a / b);
            return g;
        }

        /**
         * Get the greatest common divisor of a and b
         */
        public static long gcd(long a, long b) {
            return a >= b ? gcd0(a, b) : gcd0(b, a);
        }

        private static long gcd0(long a, long b) {
            return b == 0 ? a : gcd0(b, a % b);
        }

        public static long extgcd(long a, long b, long[] coe) {
            if (a >= b) {
                return extgcd0(a, b, coe);
            } else {
                long g = extgcd0(b, a, coe);
                long tmp = coe[0];
                coe[0] = coe[1];
                coe[1] = tmp;
                return g;
            }
        }

        private static long extgcd0(long a, long b, long[] coe) {
            if (b == 0) {
                coe[0] = 1;
                coe[1] = 0;
                return a;
            }
            long g = extgcd0(b, a % b, coe);
            long n = coe[0];
            long m = coe[1];
            coe[0] = m;
            coe[1] = n - m * (a / b);
            return g;
        }

        /**
         * Get y where x * y = 1 (% mod)
         */
        public static int inverse(int x, int mod) {
            return pow(x, mod - 2, mod);
        }

        /**
         * Get x^n(% mod)
         */
        public static int pow(int x, int n, int mod) {
            int bit = 31 - Integer.numberOfLeadingZeros(n);
            long product = 1;
            for (; bit >= 0; bit--) {
                product = product * product % mod;
                if (((1 << bit) & n) != 0) {
                    product = product * x % mod;
                }
            }
            return (int) product;
        }

        public static long longpow(long x, long n, long mod) {
            if (n == 0) {
                return 1;
            }
            long prod = longpow(x, n >> 1, mod);
            prod = modmul(prod, prod, mod);
            if ((n & 1) == 1) {
                prod = modmul(prod, x, mod);
            }
            return prod;
        }

        /**
         * Get x % mod
         */
        public static int mod(int x, int mod) {
            x %= mod;
            if (x < 0) {
                x += mod;
            }
            return x;
        }

        public static int mod(long x, int mod) {
            x %= mod;
            if (x < 0) {
                x += mod;
            }
            return (int) x;
        }

        /**
         * Get n!/(n-m)!
         */
        public static long permute(int n, int m) {
            return m == 0 ? 1 : n * permute(n - 1, m - 1);
        }

        /**
         * Put all primes less or equal to limit into primes after offset
         */
        public static int eulerSieve(int limit, int[] primes, int offset) {
            boolean[] isComp = new boolean[limit + 1];
            int wpos = offset;
            for (int i = 2; i <= limit; i++) {
                if (!isComp[i]) {
                    primes[wpos++] = i;
                }
                for (int j = offset, until = limit / i; j < wpos && primes[j] <= until; j++) {
                    int pi = primes[j] * i;
                    isComp[pi] = true;
                    if (i % primes[j] == 0) {
                        break;
                    }
                }
            }
            return wpos - offset;
        }

        /**
         * Round x into integer
         */
        public static int intRound(double x) {
            if (x < 0) {
                return -(int) (-x + 0.5);
            }
            return (int) (x + 0.5);
        }

        /**
         * Round x into long
         */
        public static long longRound(double x) {
            if (x < 0) {
                return -(long) (-x + 0.5);
            }
            return (long) (x + 0.5);
        }
    }

    public static class FastIO {
        public final StringBuilder cache = new StringBuilder();
        private final InputStream is;
        private final OutputStream os;
        private final Charset charset;
        private StringBuilder defaultStringBuf = new StringBuilder(1 << 8);
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastIO(InputStream is, OutputStream os, Charset charset) {
            this.is = is;
            this.os = os;
            this.charset = charset;
        }

        public FastIO(InputStream is, OutputStream os) {
            this(is, os, Charset.forName("ascii"));
        }

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

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

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

        public long readLong() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            long val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

        public double readDouble() {
            boolean sign = true;
            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+';
                next = read();
            }

            long val = 0;
            while (next >= '0' && next <= '9') {
                val = val * 10 + next - '0';
                next = read();
            }
            if (next != '.') {
                return sign ? val : -val;
            }
            next = read();
            long radix = 1;
            long point = 0;
            while (next >= '0' && next <= '9') {
                point = point * 10 + next - '0';
                radix = radix * 10;
                next = read();
            }
            double result = val + (double) point / radix;
            return sign ? result : -result;
        }

        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);
        }

        public int readLine(char[] data, int offset) {
            int originalOffset = offset;
            while (next != -1 && next != '\n') {
                data[offset++] = (char) next;
                next = read();
            }
            return offset - originalOffset;
        }

        public int readString(char[] data, int offset) {
            skipBlank();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (char) next;
                next = read();
            }

            return offset - originalOffset;
        }

        public int readString(byte[] data, int offset) {
            skipBlank();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (byte) next;
                next = read();
            }

            return offset - originalOffset;
        }

        public char readChar() {
            skipBlank();
            char c = (char) next;
            next = read();
            return c;
        }

        public void flush() {
            try {
                os.write(cache.toString().getBytes(charset));
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public boolean hasMore() {
            skipBlank();
            return next != -1;
        }
    }

    public static class Debug {
        private boolean allowDebug;

        public Debug(boolean allowDebug) {
            this.allowDebug = allowDebug;
        }

        public void assertTrue(boolean flag) {
            if (!allowDebug) {
                return;
            }
            if (!flag) {
                fail();
            }
        }

        public void fail() {
            throw new RuntimeException();
        }

        public void assertFalse(boolean flag) {
            if (!allowDebug) {
                return;
            }
            if (flag) {
                fail();
            }
        }

        private void outputName(String name) {
            System.out.print(name + " = ");
        }

        public void debug(String name, int x) {
            if (!allowDebug) {
                return;
            }

            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, long x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, double x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, int[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, long[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, double[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, Object x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, Object... x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.deepToString(x));
        }
    }
}