Counting Friends

Time limit1sMemory limit128 MB

Summary

Removing one of N+1 listed counts, find every entry whose removal leaves counts realizable as mutual friendships among N cows.

Level: Medium6 of 10
Topics: Graph, Sorting
Solved: No attempts yet

Problem

Farmer John has $N$ cows ( $2 \le N \le 500$ ) on the social network MooBook.

Each cow has one or more friends on MooBook. While writing down every cow's friend count, Farmer John got distracted and accidentally wrote one extra number. His list therefore has $N+1$ entries instead of $N$ .

Find every entry that could be the mistaken extra number.

Input

Line 1: integer $N$
Lines 2 through $N+2$ : one integer per line, either a cow's friend count or the extra mistaken number

Output

Line 1: integer $K$ , the number of entries that could be the extra number ( $K=0$ means no removal leaves a valid friend assignment)
Next $K$ lines: indices from 1 through $N+1$ in the input order. Print an index if removing that entry leaves $N$ counts that can be realized as mutual friendships among $N$ cows. Print indices in sorted order.

Examples1

Example 1
Input
```
4
1
2
2
1
3
```
Expected output
```
3
1
4
5
```