Team Olympiad

Source: Codeforces

Version: Phuoc Hung OJ Extended

Problem

Each student has type $t_i\in\{1,2,3\}$. A team needs one student of every type, and no student can be reused. If $c_j$ is the count of type $j$, the maximum team count is $w=\min(c_1,c_2,c_3)$. For deterministic judging, list indices of each type in increasing order and make team $k$ from the $k$-th index of types 1, 2, and 3, in that order.

Input

The first line contains $n$. The second line contains $t_1,\ldots,t_n$.

Output

Print $w$, then $w$ deterministic triples. If $w=0$, print only 0.

Subtask

Subtask 1 (20 points): $1\le n\le10$.

Subtask 2 (30 points): $1\le n\le500$.

Subtask 3 (50 points): $1\le n\le5000$.

Example

Input

7
1 3 1 3 2 1 2

Output

2
1 5 2
3 7 4

Explanation

The type-index lists are (1,3,6), (5,7), and (2,4), so two teams are produced.