Alien Microwave

A standard microwave takes the cooking time as a string in the form hhmmss, where hh, mm, and ss are two-digit integers less than 24, 60, and 60, respectively. Leading zeros in hhmmss are omitted. For example, 3 minutes is entered as 300, though 0300 or 00300 is also accepted.

If any of hh, mm, or ss exceeds its limit, the microwave rejects the input and gives an error. For example, 75 and 240000 are not accepted. In this problem, zero seconds of cooking time (written as one or more 0s) is also a valid cooking time.

When entering a time, a user may accidentally omit one digit. For example, entering 1030 (10 minutes and 30 seconds) becomes 100 (1 minute) if the digit 3 is omitted, and 030 (30 seconds) if the digit 1 is omitted. Omitting any of the four digits still gives a valid cooking time. However, 1700 (17 minutes) becomes invalid if either of the zeros is omitted. A valid cooking time that becomes invalid when exactly one digit is omitted is called an Error-Prone cooking time.

On an alien planet, a standard microwave is operated by a string $a_1a_2a_3 \dots a_n$, where each $a_i$ is a two-digit non-negative integer in base 10 that is less than $t_i$. The rules for valid and invalid cooking times still apply.

Given the limits $t_1, t_2, \dots, t_n$, find the number of Error-Prone cooking times. Leading zeros do not change a cooking time, so 066 and 66 are the same time and are counted once. Also, 0 is a valid cooking time.

The first line contains an integer $n$ ($1 \le n \le 9$), the number of time types in the alien time scheme.

Each of the next $n$ lines contains an integer $t_i$ ($1 \le t_i \le 100$), the number of partitions in the $i$th time type.

Print a single integer: the number of Error-Prone cooking times, counting each time once regardless of leading zeros.