There are students () standing in a line. Each student (1 \le i < n) reports that student i+1 is a cheater.
The following rule holds : If reports and reports , then is considered reported by both and .
Find the index of the student who is reported by the most people, and how many people reported them.
The first line of each test case contains single integer (1 \le t \le 10^4) — the number of test cases.
The only line of each test case contains single integer (1 \le n \le 10^9) — the number of students.
For each test case , Output two integers — the index of most reported student and the number of reports.
Example 1
Subtask ( points) : No additional constraints.