First Choice from One to Three

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Read choice codes until the first code in 1, 2, 3. Ignore other codes; output the first valid code and the total number of values read, including the successful read.

Input

A sequence of integers; the last is in $[1,3]$ and no preceding number is in $[1,3]$.

Output

Print two integers on one line: the first valid code and the number of reads, separated by one space.

Subtasks

• Subtask 1 (20%): At most 5 values; each value has absolute value at most 10.
• Subtask 2 (30%): At most 100 values; each value has absolute value at most 1000.
• Subtask 3 (50%): At most 100001 values; each value has absolute value at most 1000000.

Examples

Example 1

Input

0 5 2

Output

2 3

Explanation

Zero and five are invalid; two is first valid on the third read.

Example 2

Input

3

Output

3 1

Explanation

Three is valid on the first read, so the count is one.