Alien Microwave

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

When any of `hh`, `mm`,
or `ss` exceeds the limit, the microwave will
not accept it as a valid cooking time and gives an error. For
example, `75` is not accepted, nor is
`240000`. Note that for the purpose of this
problem, we assume that zero seconds of cooking time
(represented by a sequence of zero or more `0`’s) is valid.

Sometimes, one might make a mistake by omitting a digit
while entering the cooking time. For example, while entering
`1030` ($10$ minutes and $30$ seconds), omitting the digit
`3` turns the input time into `100` ($1$ minute)
instead. Omitting the digit `1` turns it into
`030` ($30$ seconds). In this case, omitting
any of the four digits will still make the resulting string a
valid cooking time. However, some other strings, while valid
cooking times themselves, can become invalid when *exactly* one of the digits is omitted. For example,
`1700` ($17$ minutes) becomes invalid if
either of the zeros is omitted. Such strings are called
*Error-Prone* cooking times.

Now, imagine some extraterrestrial planet, on which a standard microwave is operated by a string in the form $a_1a_2a_3 \ldots a_ n$, where each of $a_1$, $a_2$, …, $a_ n$ is a two-digit non-negative integer (somehow they also use base $10$) less than limits $t_1$, $t_2$, …, $t_ n$, respectively. The rules of valid and invalid cooking time still hold.

Given limits $t_1$,
$t_2$, …, $t_ n$, find the number of
*Error-Prone* cooking times. Note that leading zeros
don’t change the cooking time, so a time specification like
`066` is the same as `66`,
and should not be counted twice. Also note that $0$ is a legitimate cooking time.

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

Each of the next $n$ lines contains an integer $t_ i$ ($1 \le t_ i \le 100$), which is the number of partitions in the $i^{th}$ time type in the alien scheme.

Output a single integer, which is the number of
*Error-Prone* cooking times without leading zeros.

Sample Input 1 | Sample Output 1 |
---|---|

3 24 60 60 |
51840 |