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.

### Input

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.

### Output

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.

### Samples

input | output |
---|

2
0 1
1 0 | YES
1
2 1 2 |

5
0 1 0 1 1
1 0 1 0 1
0 1 0 1 1
1 0 1 0 1
1 1 1 1 0 | YES
2
3 1 2 5
2 3 4 |

**Problem Author: **Semyon Trifochkin