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

Statement

 Goal

The Cistercian order of monks have their own numeral system wherein any natural number less than 10,000 can be represented by a single ideograph composed of simple lines arranged in four quadrants around a "stem".

The following diagram shows the mapping between the decimal digits and their Cistercian counterparts:

0    1    2    3    4    5    6    7    8    9
__ _ _ _
| | | |\ | / | / | | | | | | | |
| | |__ | \ |/ |/ | | | | |_| |_|

These lines are mirrored (flipped horizontally and/or vertically) over the axes to represent place values other than units in the following way:

2|1
‒‒‒‒
4|3

1: ones, 2: tens, 3: hundreds, 4: thousands

As an example, here's 1337 as a Cistercian numeral:

   _
/| |
/ | |
|
|
| /
__|/

Just to crystal-clarify how the lines get reflected for each quadrant, here are the multiples of 1111 as Cistercian numerals:

__ __                        _ _           _ _           _ _
| | /|\ \ | / \ | / | | | | | | | | | | | |
| __|__ / | \ \|/ \|/ | | | | | | |_|_| |_|_|
| | | | | | | | |
| __|__ | | | | | _|_ _|_
| | \ | / /|\ /|\ | | | | | | | | | | | |
__|__ | \|/ / | \ /_|_\ | | | |_|_| | | | |_|_|

‒‒‒‒

Given a series of Cistercian numerals, display their sum (mod-10000, of course) as a Cistercian numeral.

Some helpful and interesting resources:

Numberphile's "The Forgotten Number System" (the inspiration for this puzzle): https://www.youtube.com/watch?v=9p55Qgt7Ciw
The Ciphers of the Monks: http://www.davidaking.org/Ciphers.htm
Conversion utility: https://www.dcode.fr/cistercian-numbers
Input
7 lines of ASCII art, a series of Cistercian numerals
Output
the sum of the decimal numbers represented by the numerals as a Cistercian numeral

NOTE that although the input has been padded (all numerals are 5 wide by 7 high, separated by two spaces) to aid parsing, your output should be free of any excess whitespace.
Constraints
1 ≤ N ≤ 10, where N is the number of Cistercian numerals
Example
Input
   __     __
  |      |  
  |      |  
  |      |  
  |      |  
  |      |  
  |      |  
Output
|
|__
|
|
|
|

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