Polycarpus analyzes a string called abracadabra . This string is constructed using the following algorithm: On the first step the string consists of a single character " a ". On the k -th step Polycarpus concatenates two copies of the string obtained on the ( k - 1) -th step, while inserting the k -th character of the alphabet between them. Polycarpus uses the alphabet that consists of lowercase Latin letters and digits (a total of 36 characters). The alphabet characters are numbered like this: the 1-st character is " a ", the 2-nd — " b ", ..., the 26-th — " z ", the 27-th — " 0 ", the 28-th — " 1 ", ..., the 36-th — " 9 ". Let's have a closer look at the algorithm. On the second step Polycarpus will concatenate two strings " a " and insert the character " b " between them, resulting in " aba " string. The third step will transform it into " abacaba ", and the fourth one - into " abacabadabacaba ". Thus, the string constructed on the k -th step will consist of 2 k - 1 characters. Polycarpus wrote down the string he got after 30 steps of the given algorithm and chose two non-empty substrings of it. Your task is to find the length of the longest common substring of the two substrings selected by Polycarpus. A substring s i ... j ( 1 ≤ i ≤ j ≤ | s | ) of string s = s 1 s 2 ... s | s | is a string s i s i + 1 ... s j . For example, substring s 2...4 of string s = " abacaba " equals " bac ". The string is its own substring. The longest common substring of two strings s and t is the longest string that is a substring of both s and t . For example, the longest common substring of " contest " and " systemtesting " is string " test ". There can be several common substrings of maximum length. The input consists of a single line containing four integers l 1 , r 1 , l 2 , r 2 ( 1 ≤ l i ≤ r i ≤ 10 9 , i = 1, 2 ). The numbers are separated by single spaces. l i and r i give the indices of the first and the last characters of the i -th chosen substring, correspond