CSES - KILO 2017 3/5 - Regular Bracket Sequence
  • Time limit: 1.00 s
  • Memory limit: 512 MB

As you may already know, the set S of regular bracket sequences of round and square brackets can be recursively defined as follows:

  1. \varepsilon \in S (empty sequence)
  2. A \in S \Rightarrow (A) \in S (add round brackets)
  3. A \in S \Rightarrow [A] \in S (add square brackets)
  4. A, B \in S \Rightarrow AB \in S (concatenation)

Uolevi wrote a regular bracket sequence of length n on the blackboard. The sequence contained only round brackets. Then Kaaleppi came and replaced all brackets from l-th to r-th character inclusive by the corresponding square brackets, ( by [ and ) by ]. Amazingly, the resulting sequence on the blackboard was also a regular bracket sequence.

Find any sequence which could have appeared on the blackboard as a result or determine that this story is not true.

Input

The input contains three integers: n, the length of the sequence, l, the left endpoint of the interval and r, the right endpoint of the interval.

Output

Output any regular bracket sequence which satisfies the conditions if such bracket sequence exists. Otherwise output QAQ

Constraints

  • 1 \le l \le r \le n \le 100

Examples

Input:

4 2 3

Output:

([])

Input:

4 1 2

Output:

[]()

Input:

4 1 3

Output:

QAQ