Inferring Array Size from an Omitted Size

Source: Phuoc Hung OJ

Version: Phuoc Hung OJ Extended

Problem

Consider a C array declaration whose size is omitted:

int a[] = {v0, v1, ..., v(n-1)};

The initializer list contains exactly $n$ elements. Therefore the inferred array size is

and, with 0-based indexing, the valid index set is

Output the inferred size $N$ and the largest valid index.

Input

The first line contains $n$. The second line contains exactly $n$ initializer values.

Output

Print $N$ and $N-1$.

Subtask

Subtask 1 (20 points): $1\le n\le10$.

Subtask 2 (30 points): $1\le n\le100$.

Subtask 3 (50 points): $1\le n\le1000$.

Example

Input

5
7 2 9 -1 4

Output

5 4

Explanation

There are 5 initializer elements, so the inferred size is 5 and the last valid index is 4.