Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.

Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.

Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.

Input

The only line of the input contains a single integer n (2 ≤ n ≤ 1018) — the number of players to participate in the tournament.

Output

Print the maximum number of games in which the winner of the tournament can take part.

Examples

Input

2


Output

1


Input

3


Output

2


Input

4


Output

2


Input

10


Output

4

Note

In all samples we consider that player number 1 is the winner.

In the first sample, there would be only one game so the answer is 1.

In the second sample, player 1 can consequently beat players 2 and 3. 

In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners.
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.lang.reflect.Constructor;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.InputMismatchException;
import java.util.StringTokenizer;

public class CodeA {
  private static final boolean SHOULD_BUFFER_OUTPUT = false;

  static final SuperWriter sw = new SuperWriter(System.out);

  static final SuperScanner sc = new SuperScanner();

  static BigInteger[] dp;

  static BigInteger needed(int n) {
    if (dp[n] != null) {
      return dp[n];
    }
    if (n == 0) {
      return dp[n] = BigInteger.ONE;
    }
    BigInteger answer = needed(0);
    for (int i = 0; i < n - 1; i++) {
      answer = answer.add(needed(i));
    }
    return dp[n] = answer.add(BigInteger.ONE);
  }

  public static void main() {
    dp = new BigInteger[100];
    long n = sc.nextLong();
    for (int i = 0; true; i++) {
      BigInteger possible = needed(i);
      if (possible.compareTo(BigInteger.valueOf(n)) > 0) {
        sw.printLine(i - 1);
        return;
      }
    }
  }

  static class LineScanner extends Scanner {
    private StringTokenizer st;

    public LineScanner(String input) {
      st = new StringTokenizer(input);
    }

    @Override
    public String next() {
      return st.hasMoreTokens() ? st.nextToken() : null;
    }

    @Override
    public String nextLine() {
      throw new RuntimeException("not supported");
    }

    public boolean hasNext() {
      return st.hasMoreTokens();
    }

    private final ArrayList<Object> temp = new ArrayList<Object>();

    private void fillTemp() {
      while (st.hasMoreTokens()) {
        temp.add(st.nextToken());
      }
    }

    public String[] asStringArray() {
      fillTemp();
      String[] answer = new String[temp.size()];
      for (int i = 0; i < answer.length; i++) {
        answer[i] = (String) temp.get(i);
      }
      temp.clear();
      return answer;
    }

    public int[] asIntArray() {
      fillTemp();
      int[] answer = new int[temp.size()];
      for (int i = 0; i < answer.length; i++) {
        answer[i] = Integer.parseInt((String) temp.get(i));
      }
      temp.clear();
      return answer;
    }

    public long[] asLongArray() {
      fillTemp();
      long[] answer = new long[temp.size()];
      for (int i = 0; i < answer.length; i++) {
        answer[i] = Long.parseLong((String) temp.get(i));
      }
      temp.clear();
      return answer;
    }

    public double[] asDoubleArray() {
      fillTemp();
      double[] answer = new double[temp.size()];
      for (int i = 0; i < answer.length; i++) {
        answer[i] = Double.parseDouble((String) temp.get(i));
      }
      temp.clear();
      return answer;
    }
  }

  static class SuperScanner extends Scanner {
    private InputStream stream;
    private byte[] buf = new byte[8096];
    private int curChar;
    private int numChars;

    public SuperScanner() {
        this.stream = System.in;
    }

    public int read() {
        if (numChars == -1)
            return -1;
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }
    
    public static boolean isWhitespace(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public static boolean isLineEnd(int c) {
      return c == '\n' || c == -1;
    }
    
    private final StringBuilder sb = new StringBuilder();
    
    @Override
    public String next() {
      int c = read();
      while (isWhitespace(c)) {
          if (c == -1) {
            return null;
          }
          c = read();
      }
      sb.setLength(0);
      do {
          sb.append((char) c);
          c = read();
      } while (!isWhitespace(c));
      return sb.toString();
    }

    @Override
    public String nextLine() {
      sb.setLength(0);
      int c;
      while (true) {
        c = read();
        if (!isLineEnd(c)) {
          sb.append((char) c);
        } else {
          break;
        }
      }
      if (c == -1 && sb.length() == 0) {
        return null;
      } else {
        if (sb.length() > 0 && sb.charAt(sb.length() - 1) == '\r') {
          return sb.substring(0, sb.length() - 1);
        } else {
          return sb.toString();
        }
      }
    }

    public LineScanner nextLineScanner() {
      String line = nextLine();
      if (line == null) {
        return null;
      } else {
        return new LineScanner(line);
      }
    }

    public LineScanner nextNonEmptyLineScanner() {
      while (true) {
        String line = nextLine();
        if (line == null) {
          return null;
        } else if (!line.isEmpty()) {
          return new LineScanner(line);
        }
      }
    }

    @Override
    public int nextInt() {
        int c = read();
        while (isWhitespace(c)) {
            c = read();
        }
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res = (res << 3) + (res << 1);
            res += c - '0';
            c = read();
        } while (!isWhitespace(c));
        return res * sgn;
    }

    @Override
    public long nextLong() {
        int c = read();
        while (isWhitespace(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res = (res << 3) + (res << 1);
            res += c - '0';
            c = read();
        } while (!isWhitespace(c));
        return res * sgn;
    }
  }
  
  static abstract class Scanner {

    public abstract String next();

    public abstract String nextLine();

    public int nextIntOrQuit() {
      Integer n = nextInteger();
      if (n == null) {
        sw.close();
        System.exit(0);
      }
      return n.intValue();
    }

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

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

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

    public int[] nextIntArray(int n) {
      int[] res = new int[n];
      for (int i = 0; i < res.length; i++)
        res[i] = nextInt();
      return res;
    }

    public long[] nextLongArray(int n) {
      long[] res = new long[n];
      for (int i = 0; i < res.length; i++)
        res[i] = nextLong();
      return res;
    }

    public double[] nextDoubleArray(int n) {
      double[] res = new double[n];
      for (int i = 0; i < res.length; i++)
        res[i] = nextDouble();
      return res;
    }

    public void sortIntArray(int[] array) {
      Integer[] vals = new Integer[array.length];
      for (int i = 0; i < array.length; i++)
        vals[i] = array[i];
      Arrays.sort(vals);
      for (int i = 0; i < array.length; i++)
        array[i] = vals[i];
    }

    public void sortLongArray(long[] array) {
      Long[] vals = new Long[array.length];
      for (int i = 0; i < array.length; i++)
        vals[i] = array[i];
      Arrays.sort(vals);
      for (int i = 0; i < array.length; i++)
        array[i] = vals[i];
    }

    public void sortDoubleArray(double[] array) {
      Double[] vals = new Double[array.length];
      for (int i = 0; i < array.length; i++)
        vals[i] = array[i];
      Arrays.sort(vals);
      for (int i = 0; i < array.length; i++)
        array[i] = vals[i];
    }

    public String[] nextStringArray(int n) {
      String[] vals = new String[n];
      for (int i = 0; i < n; i++)
        vals[i] = next();
      return vals;
    }

    public Integer nextInteger() {
      String s = next();
      if (s == null)
        return null;
      return Integer.parseInt(s);
    }

    public int[][] nextIntMatrix(int n, int m) {
      int[][] ans = new int[n][];
      for (int i = 0; i < n; i++)
        ans[i] = nextIntArray(m);
      return ans;
    }

    public char[][] nextGrid(int r) {
      char[][] grid = new char[r][];
      for (int i = 0; i < r; i++)
        grid[i] = next().toCharArray();
      return grid;
    }

    public static <T> T fill(T arreglo, int val) {
      if (arreglo instanceof Object[]) {
        Object[] a = (Object[]) arreglo;
        for (Object x : a)
          fill(x, val);
      } else if (arreglo instanceof int[])
        Arrays.fill((int[]) arreglo, val);
      else if (arreglo instanceof double[])
        Arrays.fill((double[]) arreglo, val);
      else if (arreglo instanceof long[])
        Arrays.fill((long[]) arreglo, val);
      return arreglo;
    }

    public <T> T[] nextObjectArray(Class<T> clazz, int size) {
      @SuppressWarnings("unchecked")
      T[] result = (T[]) java.lang.reflect.Array.newInstance(clazz, size);
      for (int c = 0; c < 3; c++) {
        Constructor<T> constructor;
        try {
          if (c == 0)
            constructor = clazz.getDeclaredConstructor(Scanner.class,
                Integer.TYPE);
          else if (c == 1)
            constructor = clazz.getDeclaredConstructor(Scanner.class);
          else
            constructor = clazz.getDeclaredConstructor();
        } catch (Exception e) {
          continue;
        }
        try {
          for (int i = 0; i < result.length; i++) {
            if (c == 0)
              result[i] = constructor.newInstance(this, i);
            else if (c == 1)
              result[i] = constructor.newInstance(this);
            else
              result[i] = constructor.newInstance();
          }
        } catch (Exception e) {
          throw new RuntimeException(e);
        }
        return result;
      }
      throw new RuntimeException("Constructor not found");
    }

    public Collection<Integer> wrap(int[] as) {
      ArrayList<Integer> ans = new ArrayList<Integer>();
      for (int i : as)
        ans.add(i);
      return ans;
    }

    public int[] unwrap(Collection<Integer> collection) {
      int[] vals = new int[collection.size()];
      int index = 0;
      for (int i : collection)
        vals[index++] = i;
      return vals;
    }

    int testCases = Integer.MIN_VALUE;

    boolean testCases() {
      if (testCases == Integer.MIN_VALUE) {
        testCases = nextInt();
      }
      return --testCases >= 0;
    }
  }

  static class SuperWriter {

    private final PrintWriter writer;

    public SuperWriter(OutputStream outputStream) {
      writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public SuperWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void close() {
        writer.flush();
        writer.close();
    }

    public void printLine(String line) {
      writer.println(line);
      if (!SHOULD_BUFFER_OUTPUT) {
        writer.flush();
      }
    }

    public void printLine(int... vals) {
      if (vals.length == 0) {
        writer.println();
      } else {
        writer.print(vals[0]);
        for (int i = 1; i < vals.length; i++)
          writer.print(" ".concat(String.valueOf(vals[i])));
        writer.println();
      }
      if (!SHOULD_BUFFER_OUTPUT) {
        writer.flush();
      }
    }

    public void printLine(long... vals) {
      if (vals.length == 0) {
        writer.println();
      } else {
        writer.print(vals[0]);
        for (int i = 1; i < vals.length; i++)
          writer.print(" ".concat(String.valueOf(vals[i])));
        writer.println();
      }
      if (!SHOULD_BUFFER_OUTPUT) {
        writer.flush();
      }
    }

    public void printLine(double... vals) {
      if (vals.length == 0) {
        writer.println();
      } else {
        writer.print(vals[0]);
        for (int i = 1; i < vals.length; i++)
          writer.print(" ".concat(String.valueOf(vals[i])));
        writer.println();
      }
      if (!SHOULD_BUFFER_OUTPUT) {
        writer.flush();
      }
    }

    public void printLine(int prec, double... vals) {
      if (vals.length == 0) {
        writer.println();
      } else {
        String precision = "%." + prec + "f";
        writer.print(String.format(precision, vals[0]).replace(',', '.'));
        precision = " " + precision;
        for (int i = 1; i < vals.length; i++)
          writer.print(String.format(precision, vals[i]).replace(',', '.'));
        writer.println();
      }
      if (!SHOULD_BUFFER_OUTPUT) {
        writer.flush();
      }
    }

    public <E> void printLine(Collection<E> vals) {
      if (vals.size() == 0) {
        writer.println();
      } else {
        int i = 0;
        for (E val : vals) {
          if (i++ == 0) {
            writer.print(val.toString());
          } else {
            writer.print(" ".concat(val.toString()));
          }
        }
        writer.println();
      }
      if (!SHOULD_BUFFER_OUTPUT) {
        writer.flush();
      }
    }

    public void printSimple(String value) {
      writer.print(value);
      if (!SHOULD_BUFFER_OUTPUT) {
        writer.flush();
      }
    }

    public boolean ifZeroExit(Number... values) {
    	for (Number number : values) {
    		if (number.doubleValue() != 0.0d || number.longValue() != 0) {
    			return false;
    		}
    	}
    	close();
    	System.exit(0);
    	return true;
    }
  }


  public static void main(String[] args) {
    main();
    sw.close();
  }
}
