Let N, x and y be positive integers such that N = x + y, 2 &lt; x &lt; 10 and 14 &lt; y &lt; 23. If N &gt; 25, then how many distinct values are possible for N?

Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are possible for N?

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