Piegirl got bored with binary, decimal and other integer based counting systems. Recently she discovered some interesting properties about number <image>, in particular that q2 = q + 1, and she thinks it would make a good base for her new unique system. She called it "golden system". In golden system the number is a non-empty string containing 0's and 1's as digits. The decimal value of expression a0a1...an equals to <image>.

Soon Piegirl found out that this system doesn't have same properties that integer base systems do and some operations can not be performed on it. She wasn't able to come up with a fast way of comparing two numbers. She is asking for your help.

Given two numbers written in golden system notation, determine which of them has larger decimal value.

Input

Input consists of two lines — one for each number. Each line contains non-empty string consisting of '0' and '1' characters. The length of each string does not exceed 100000.

Output

Print ">" if the first number is larger, "<" if it is smaller and "=" if they are equal.

Examples

Input

1000
111


Output

&lt;


Input

00100
11


Output

=


Input

110
101


Output

&gt;

Note

In the first example first number equals to <image>, while second number is approximately 1.6180339882 + 1.618033988 + 1 ≈ 5.236, which is clearly a bigger number.

In the second example numbers are equal. Each of them is  ≈ 2.618.

import java.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * 4 4
 * 1 5 3 4
 * 1 2
 * 1 3
 * 2 3
 * 3 3
 *
 *
 * @author pttrung
 */
public class A {

    public static long Mod = (long) (1e9) + 7;
    public static long[][] dp;
    static int time = 1;

    public static void main(String[] args) throws FileNotFoundException {

        //PrintWriter out = new PrintWriter(new FileOutputStream(new File("output.txt")));
        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        String[] data = new String[2];
        int[] l = new int[2];
        for (int i = 0; i < 2; i++) {
            data[i] = in.next();
            l[i] = data[i].length() ;
        }
        int[] c = new int[Math.max(l[0], l[1]) + 1];
        for (int i = 0; i < l[0]; i++) {
            if (data[0].charAt(i) == '1') {
                c[l[0] - i]++;
               // System.out.println("HE HE");
            }
        }
        for (int i = 0; i < l[1]; i++) {
            if (data[1].charAt(i) == '1') {
                c[l[1] - i]--;
            }
        }
        
        int pos = -1;
        int neg = -1;
        for (int i = c.length - 1; i >= 0 && (pos == -1 || neg == -1); i--) {
            if (c[i] > 0) {
                if (pos == -1) {
                    pos = i;
                }
            } else if (c[i] < 0) {
                if (neg == -1) {
                    neg = i;
                }
            }
        }
       // System.out.println(Arrays.toString(c));
        if (pos == -1 || neg == -1) {
            if (pos == -1) {
                if (neg == -1) {
                    out.println("=");
                } else {
                    out.println("<");
                }
            } else {
                out.println(">");
            }
        } else {
            boolean ok = true;
            
            int start = Math.max(pos, neg);
            for (int i = start; i >= 0 && ok; i--) {
               // System.out.println(Arrays.toString(c));
                if (c[i] > 0) {

                    int cur = c[i];
                    for (int j = i; j >= 0 && cur > 0; j--) {
                        if (c[j] < 0) {
                            if (-c[j] <= cur) {
                                cur += c[j];
                                c[j] = 0;
                                if (j - 2 >= 0) {
                                    c[j - 2] += cur;
                                }
                            } else {
                                c[j] += cur;
                                cur = 0;
                            }
                        }else{
                            if(j - 2 >= 0){
                                c[j - 2] += cur;
                            }
                        }
                    }
                    if (cur > 0) {
                        ok = false;
                        out.println(">");
                       
                    }
                } else if (c[i] < 0) {
                    int cur = c[i];
                    for (int j = i ; j >= 0 && cur < 0; j--) {
                        if (c[j] > 0) {
                            if (c[j] <= -cur) {
                                cur += c[j];
                                c[j] = 0;
                                if (j - 2 >= 0) {
                                    c[j - 2] += cur;
                                }
                            } else {
                                c[j] += cur;
                                cur = 0;
                            }
                        }else{
                            if(j - 2 >= 0){
                                c[j - 2] += cur;
                            }
                        }
                    }
                    if (cur < 0) {
                        ok = false;
                        out.println("<");
                       
                    }
                }
            }
            if (ok) {
                out.println("=");
            }
        }

        out.close();

    }

    static long[] cal(int p) {
        if (p == 0) {
            return new long[]{0, 1};
        } else if (p == 1) {
            return new long[]{1, 0};
        } else if (p == 2) {
            return new long[]{1, 1};
        }
        if (dp[p][0] != -1) {
            return dp[p];
        }
        long[] result = new long[2];
        long[] tmp = cal(p - 2);
        result[0] = tmp[0] + tmp[1];

        result[1] = tmp[1];
        result[0] += tmp[0];
        result[1] += tmp[0];
        return dp[p] = result;
    }

    static int find(int index, int[] u) {
        if (index != u[index]) {
            return u[index] = find(u[index], u);
        }
        return index;
    }

    public static long pow(int a, int b, long mod) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long v = pow(a, b / 2, mod);
        if (b % 2 == 0) {
            return (v * v) % mod;
        } else {
            return (((v * v) % mod) * a) % mod;
        }
    }

    public static int[][] powSquareMatrix(int[][] A, long p) {
        int[][] unit = new int[A.length][A.length];
        for (int i = 0; i < unit.length; i++) {
            unit[i][i] = 1;
        }
        if (p == 0) {
            return unit;
        }
        int[][] val = powSquareMatrix(A, p / 2);
        if (p % 2 == 0) {
            return mulMatrix(val, val);
        } else {
            return mulMatrix(A, mulMatrix(val, val));
        }

    }

    public static int[][] mulMatrix(int[][] A, int[][] B) {
        int[][] result = new int[A.length][B[0].length];
        for (int i = 0; i < result.length; i++) {
            for (int j = 0; j < result[0].length; j++) {
                long temp = 0;
                for (int k = 0; k < A[0].length; k++) {

                    temp += ((long) A[i][k] * B[k][j] % Mod);
                    temp %= Mod;
                }
                temp %= Mod;
                result[i][j] = (int) temp;
            }
        }

        return result;
    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;




    }

    static class FT {

        int[] data;

        FT(int n) {
            data = new int[n];
        }

        void update(int index, int val) {
            // System.out.println("UPDATE INDEX " + index);
            while (index < data.length) {
                data[index] += val;
                index += index & (-index);

                //    System.out.println("NEXT " +index);
            }
        }

        int get(int index) {
            //  System.out.println("GET INDEX " + index);
            int result = 0;
            while (index > 0) {
                result += data[index];
                index -= index & (-index);
                // System.out.println("BACK " + index);
            }
            return result;
        }
    }

    static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        } else {
            return gcd(b, a % b);
        }
    }

    static long pow(long a, int b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {

            return val * val % Mod;
        } else {
            return (val * val % Mod) * a % Mod;
        }
    }

//    static Point intersect(Point a, Point b, Point c) {
//        double D = cross(a, b);
//        if (D != 0) {
//            return new Point(cross(c, b) / D, cross(a, c) / D);
//        }
//        return null;
//    }
//
//    static Point convert(Point a, double angle) {
//        double x = a.x * cos(angle) - a.y * sin(angle);
//        double y = a.x * sin(angle) + a.y * cos(angle);
//        return new Point(x, y);
//    }
    static Point minus(Point a, Point b) {
        return new Point(a.x - b.x, a.y - b.y);
    }
//
//    static Point add(Point a, Point b) {
//        return new Point(a.x + b.x, a.y + b.y);
//    }
//

    /**
     * Cross product ab*ac
     *
     * @param a
     * @param b
     * @param c
     * @return
     */
    static double cross(Point a, Point b, Point c) {
        Point ab = new Point(b.x - a.x, b.y - a.y);
        Point ac = new Point(c.x - a.x, c.y - a.y);
        return cross(ab, ac);
    }

    static double cross(Point a, Point b) {
        return a.x * b.y - a.y * b.x;
    }

    /**
     * Dot product ab*ac;
     *
     * @param a
     * @param b
     * @param c
     * @return
     */
    static long dot(Point a, Point b, Point c) {
        Point ab = new Point(b.x - a.x, b.y - a.y);
        Point ac = new Point(c.x - a.x, c.y - a.y);
        return dot(ab, ac);
    }

    static long dot(Point a, Point b) {
        long total = a.x * b.x;
        total += a.y * b.y;
        return total;
    }

    static double dist(Point a, Point b) {
        long total = (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
        return Math.sqrt(total);
    }

    static long norm(Point a) {
        long result = a.x * a.x;
        result += a.y * a.y;
        return result;
    }

    static double dist(Point a, Point b, Point x, boolean isSegment) {
        double dist = cross(a, b, x) / dist(a, b);
        // System.out.println("DIST " + dist);

        if (isSegment) {
            Point ab = new Point(b.x - a.x, b.y - a.y);

            long dot1 = dot(a, b, x);
            long norm = norm(ab);
            double u = (double) dot1 / norm;
            if (u < 0) {
                return dist(a, x);
            }

            if (u > 1) {
                return dist(b, x);
            }
        }
        return Math.abs(dist);




    }

    static long squareDist(Point a, Point b) {
        long x = a.x - b.x;
        long y = a.y - b.y;
        return x * x + y * y;
    }

    static class Point {

        int x, y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public String toString() {
            return "Point{" + "x=" + x + ", y=" + y + '}';
        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            //System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //br = new BufferedReader(new FileReader(new File("A-large (2).in")));
        }

        public String next() {


            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}
