The 4B class went to a zoo with their teacher. Unfortunately for her, there’s a lot of children, and she’s alone. To make it easier for herself, she decided to separate children into groups of 2 or 3 students. Each student may only be assigned to one group! However, this is difficult, because each child will only want to be in a group with someone they know.

There are n students in the 4B class. The teacher knows which students are friends (the friendship is always bidirectional!) and that each student is a friend of at least ⌈ⁿ⁄₂⌉ other students (⌈x⌉  is the smallest integer that is greater than or equal to x). Help the teacher to separate children into groups.

The first line contains a single integer n (2 ≤ n ≤ 1000).

Each of the next n lines contains space-separated integers m_{i, 1}, m_{i, 2}, …, m_{i, n}. These integers are all either 0 or 1 (m_{i, j} ∈ {0, 1}). If m_{i, j} = 1, then i-th and j-th students are friends, otherwise they aren’t. It is guaranteed that m_{i, j} = m_{j, i} and m_{i, i} = 0.

In the first line, write “YES” (without quotes) if the students can be separated into groups, otherwise output “NO”. In the case of “NO” nothing else needs to be written.

In the second line, write k — the number of groups.

Then output k more lines, i-th of them should start with a_i — the size of the i-th group. Then write a_i integers in the same line — indices of students in the i-th group. The students are numbered from 1 to n in the same order they are given in the input.