Do you think that counting is easy? This is not the case when you don't fully understand objects that you are counting. Let's call a \textbf{2N}-digit integer \textbf{X} (possibly with leading zeroes) amusing if two \textbf{N}-digit integers \textbf{a} and \textbf{b} (again, possibly with leading zeroes) exist such that \textbf{a} + \textbf{b} = \textbf{10^N} and \textbf{S_d}(\textbf{X}) = \textbf{S_d}(\textbf{a}) + \textbf{S_d}(\textbf{b}) holds for every digit \textbf{d}, where \textbf{S_d}(\textbf{P}) (\textbf{0 }≤ \textbf{d }≤ \textbf{9}) is the number of occurrences of digit \textbf{d} in the decimal representation of \textbf{P}. For example, numbers \textbf{46} (\textbf{4} + \textbf{6}= \textbf{10^1}), \textbf{9820} (\textbf{98} + \textbf{02} = \textbf{10^2}) and \textbf{08362090} (\textbf{6020} + \textbf{3980} = \textbf{10^4}) are amusing. You are given a sequence of digits and question marks of an even length. Find the number of ways to replace question marks with digits to get an amusing number, modulo \textbf{10^9} + \textbf{7}. \InputFile The only line contains a non-empty sequence of digits and question marks. The length of the sequence is even and doesn't exceed \textbf{10^5}. The number of question marks doesn't exceed \textbf{1000}. \OutputFile Print the sought number of ways modulo \textbf{10^9} + \textbf{7}.