Problem 67. Sequence of Signs

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We want to arrange twenty numbers -10, -9, -8, …, -1, 1, 2, 3, …, 10 from left to right in a way that the signs of the sum of the prefixes is as follows:

- + + - - - + + - - - + - + - + - - - +

That is, the first number is negative, the sum of the first two numbers is positive, the sum of the first three numbers is positive, the sum of the first four numbers is negative, ..., the sum of the first nineteen numbers is negative, and finally the total sum of all 20 numbers is positive.

We consider 0 as a positive number.

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Here is an example of the arrangement: -1 1 2 -3 -2 -4 7 3 -5 -6 4 5 -7 6 -8 8 -9 -10 9 10.