Even if it's a really easy question, she won't be able to answer it— Perfect Memento in Strict Sense

Cirno's perfect bitmasks classroom has just started!

Cirno gave her students a positive integer $x$. As an assignment, her students need to find the minimum positive integer $y$, which satisfies the following two conditions:

$$x\ \texttt{and}\ y \gt 0$$ $$x\ \texttt{xor}\ y \gt 0$$

Where $\texttt{and}$ is the bitwise AND operation, and $\texttt{xor}$ is the bitwise XOR operation.

Among the students was Mystia, who was truly baffled by all these new operators. Please help her!

Input

The first line of input contains a single integer $t$ ($1 \leq t \leq 10^3$) — the number of input test cases.

For each test case, the only line of input contains one integer $x$ ($1 \leq x \leq 2^{30}$).

Output

For each test case, print a single integer — the minimum number of $y$.

Note

Test case 1:

$1\; \texttt{and}\; 3=1 \gt 0$, $1\; \texttt{xor}\; 3=2 \gt 0$.

Test case 2:

$2\; \texttt{and}\; 3=2 \gt 0$, $2\; \texttt{xor}\; 3=1 \gt 0$.