Grandparents

A grandfather and a grandmother are $N$ years old in total. The grandfather's current age is twice the grandmother's age back when the grandfather was as old as the grandmother is now. How old is the grandmother?

The first line contains an integer $T$, the number of test cases. Each of the next $T$ lines contains one positive integer $N$, the combined age of the two grandparents. $N$ does not exceed an upper limit $G$.

For each test case, print the grandmother's age rounded to the nearest integer, one per line — unless the test number (counting from $1$) is divisible by $X$, in which case print AMPPZ 2010 on that line instead (the quotation marks are only for emphasis and must not appear in the output).

• $X$ — the largest integer whose square and cube, written side by side, together use every digit from $0$ to $9$ exactly once.
• $G$ — equal to $22 \cdot i$, where $i$ is the fourth number from the left of the ninth sequence, in lexicographic order, among all ways of filling a $3\times 3$ square with the numbers $0, 1, \ldots, 8$ so that the sums along every row and every column are all equal. The sequence $a_0, \ldots, a_8$ corresponds to the square laid out as:

a0 a1 a2
a3 a4 a5
a6 a7 a8

• $T$ — no greater than the largest divisor of $A = 1000036000099$ that is smaller than $A$.