Team Olympiad · Interview Problem

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Team Olympiad

Form teams of three students so that each team contains one member from each skill type 1, 2, and 3.

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Problem Statement

Problem

You are given $n$ students. Each student has a skill type: $1 $, \$ 2 $, or \$ 3$.

Your task is to form as many teams as possible such that each team contains exactly three students and the three students on a team have different skill types — one student of type $1 $, one of type \$ 2 $, and one of type \$ 3$.

After choosing the teams, output the number of teams and the indices of the students in each team.

Goal

Maximize the number of valid teams.

Notes

Each student can belong to at most one team.
Any valid assignment with the maximum number of teams is accepted.

Input Format

The first line contains an integer $n$ .
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ , where each $a_i \in \{1,2,3\}$ .

Output Format

On the first line, output the maximum number of teams.
Then output that many lines, each containing three integers: the indices of students in one team.
The order of teams and the order of indices inside a team do not matter, as long as every team is valid.

Constraints

$1 \le n \le 100$
$a_i \in \{1,2,3\}$

Examples

Sample cases returned by the problem API.

Example 1

Input

7
1 3 1 3 2 1 2

Output

2
3 5 1
6 7 2

Explanation

There are three students of type 1, two of type 2, and two of type 3, so at most 2 teams can be formed. One valid choice is (3,5,1) and (6,7,2), where each team has one student of each type.

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