Let \( \{ x_1, x_2 , \ldots, x_{100} \} \) be a permutation of \( \{ 1, 2, \ldots 100 \} \). What is the minimum, over all permutations, of \[ \max_{i=1 \mbox{ to }91 } x_{i} + x_{i+1} + x_{i+2} + \ldots + x_{i+9} ? \]

Note: A permutation is a rearrangement of all of the numbers in the sequence.

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