408976: GYM103401 E Power tower

Consider an array {$$$a_n$$$}, where $$$a_1$$$=2 and $$$a_n$$$=$$$2^{a_{n-1}}$$$, for all n>=2. As you can imagine, while n is huge enough, $$$a_n$$$ looks like a tower, and we call this tower "Power tower".

But as we all know, computer has difficulty in dealing with big integers, so he defines another array $$$b_n$$$=$$$a_n$$$ It is easy to prove that {$$$b_n$$$} is a convergent array.(In other words, $$${\lim_{n \to+ \infty}}b_n$$$ exists). Your task is to calculate the $$${\lim_{n \to+ \infty}}b_n$$$.

The input has manly lines. The first line contains an postive integer T，means the number of limit you need to calculate. The next T lines，Each lines contains an postive integer p. （T<=10^3, p<= 10^7）

The output contains T lines, for each line, you need to output an postive integer p, means the value of $$${\lim_{n \to+ \infty}}b_n$$$.

3
2
3
6

0
1
4