Always divisible by 271

Choose a number with 5 different numbers. Do not use the zero.
Write underneath all possible permutations of those numbers.
You'll get a list of 120 numbers. (120 = 5! = 1 × 2 × 3 × 4 × 5 permutations.)
Show that the sum of these 120 numbers is divisible by 271 always.
Tip: Use a spreadsheet or spreadsheet. But only if you want to check.
The proof is very short!

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