Set

You have ~q~ queries and an empty set. Each query is of the form:

• ADD x: Add x to the set
• ERASE x: Erase x from the set
• NTH n: Output the n-th smallest number in the set (1-indexed)
• MIN: Output the minimum value in the set
• MAX: Output the maximum value in the set

Constraints

~1 \le q \le 10^5~

~1 \le x \le 10^9~

Common sense constraints should hold (~n \le \left|\text{set}\right|~).

Example 1

Input

5
ADD 1
ADD 2
NTH 2
MIN
MAX

Input

2
1
2