Today, Marisa visited Alice at her house. Alice was busy assigning chores to her collection of $n$ dolls, with $n$ chores in total. She knows that if the $i^{th}$ doll perform the $j^{th}$ chore, the efficiency would be $A_{i,j}$. The efficiency of $n$ dolls equal to the minimum efficiency among the dolls. A doll can be assigned at most $1$ chore, and a chore can be assign at most $1$ times.
However, Alice does not know the maximum efficiency possible. Therefore, she has asked Marisa for help, and Marisa is turning to you for assistance.
### Input
- The first line contains an integer $n$.
- The next $n$ lines, the $i^{th}$ line contains $n$ integers $A_{i,j}$.
### Output
- The first line print the maximum efficiency to complete $n$ chores.
- The next $n$ lines, the $i^{th}$ line is the chore to which doll $i$ was assigned. If there are multiple ways to arrange chores, print any.
### Constraints
- $1 \le n \le 200$.
- $1 \le A_{i,j} \le 10^9$.
### Example
Input:
```
4
9 4 4 12
8 7 8 13
2 2 8 3
6 7 3 7
```
Output:
```
7
1
2
3
4
```
