Practice Parsing and Recursion with the exercise "Function notation"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Statement

Goal

Given a function expressed exclusively using function compositions and function sums, rewrite it by replacing the composition operator . with the reverse composition operator |>.

The reverse function composition operator behaves, unsurprisingly, by reversing the order of function application, that is:


(f |> g)(x) = g(f(x))

Examples:


f . g         --   g |> f
f + g         --   f + g
f . g + h     --   g |> f + h
(f + h) . g   --   g |> (f + h)
f . (g + h)   --   (g + h) |> f
g + f . h     --   g + h |> f

Notes:
(1) Function names are only one lowercase English letter.
(2) The + and . operators are given between spaces for easier visualization.
(3) As shown in the examples, parentheses are relevant.
(4) The expressions are well formed. They don't contain unnecessary parentheses like f . (( g + h )) or consecutive + signs etc.
(5) For debugging, notice how the transformation from . to |> is symmetric, and that the same logic, from |> to . should give back the original expression.

Input

Line 1: A string function representing a function expressed exclusively using function compositions and function sums.

Output

One line containing the original function rewritten with the |> operator.

Constraints

Function names are only one lowercase English letter.
0 < length function < 256

Example

Input

f . g

Output

g |> f

Solve it

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