human
Bishwock is a chess figure that consists of three squares resembling an "L-bar". This figure can be rotated by 90, 180 and 270 degrees so it can have four possible states:
    
    
      
    XX   XX   .X   X.  
    X.   .X   XX   XX  
    

Bishwocks don't attack any squares and can even occupy on the adjacent squares as long as they don't occupy the same square. 

Vasya has a board with 2× n squares onto which he wants to put some bishwocks. To his dismay, several squares on this board are already occupied by pawns and Vasya can't put bishwocks there. However, pawns also don't attack bishwocks and they can occupy adjacent squares peacefully.

Knowing the positions of pawns on the board, help Vasya to determine the maximum amount of bishwocks he can put onto the board so that they wouldn't occupy the same squares and wouldn't occupy squares with pawns.

Input

The input contains two nonempty strings that describe Vasya's board. Those strings contain only symbols "0" (zero) that denote the empty squares and symbols "X" (uppercase English letter) that denote the squares occupied by pawns. Strings are nonempty and are of the same length that does not exceed 100.

Output

Output a single integer — the maximum amount of bishwocks that can be placed onto the given board.

Examples

Input

00
00

Output

1

Input

00X00X0XXX0
0XXX0X00X00

Output

4

Input

0X0X0
0X0X0

Output

0

Input

0XXX0
00000

Output

2
Solve the task in PYTHON3.
 Write me a Python code to determine the maximum amount of bishwocks he can put onto the board so that they wouldn't occupy the same squares and wouldn't occupy squares with pawns?
assistant
#Here is Python code to determine the maximum amount of bishwocks he can put onto the board so that they wouldn't occupy the same squares and wouldn't occupy squares with pawns.

import itertools
import bisect
import math
from collections import *
import os
import sys
from io import BytesIO, IOBase

ii = lambda: int(input())
lmii = lambda: list(map(int, input().split()))
li = lambda: list(input())
mii = lambda: map(int, input().split())
msi = lambda: map(str, input().split())

def main():
    a = li()
    b = li()
    n = len(a)
    ans = 0
    for i in range(n):
        if a[i] == "0":
            ans += 1
            if i - 1 >= 0 and a[i] == b[i] == b[i - 1]:
                a[i] = b[i] = b[i - 1] = "X"
            elif i + 1 < n and b[i] == b[i + 1] == a[i + 1] == a[i]:
                a[i] = b[i] = a[i + 1] = "X"
            elif i + 1 < n and a[i] == b[i] == b[i + 1]:
                a[i] = b[i] = b[i + 1] = "X"
            elif i + 1 < n and a[i] == b[i + 1] == a[i + 1]:
                a[i] = b[i + 1] = a[i + 1] = "X"
            elif i + 1 < n and a[i] == b[i] == a[i + 1]:
                a[i] = b[i] = a[i + 1] = "X"
            else:
                ans -= 1
    print(ans)
    pass

BUFSIZE = 8192

class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def...