Containers

There are $n$ containers ($1 \le n \le 4$). At the start every container is completely full of water. The capacity of the $i$-th container is an integer $o_i$ liters, with $1 \le o_i \le 49$.

Three kinds of moves are allowed:

• Pour the whole contents of one container into another. This is allowed only when the destination has enough remaining room to hold all of it.
• Fill one container up to its capacity using water from another container. (Used when the source holds more water than the destination's remaining room; the destination becomes full and the leftover stays in the source.)
• Empty the whole contents of one container into a drain.

Given the capacity of every container and the requested final amount of water in every container, decide whether some sequence of allowed moves reaches that final state. If it does, output the minimum number of moves; otherwise output NIE.

The first line contains one integer $n$, the number of containers ($1 \le n \le 4$). The second line contains $n$ integers $o_1, \dots, o_n$ separated by single spaces, where $o_i$ is the capacity of the $i$-th container ($1 \le o_i \le 49$). The third line contains $n$ integers $w_1, \dots, w_n$ separated by single spaces, where $w_i$ is the requested final amount of water in the $i$-th container ($0 \le w_i \le o_i$).

If the requested final state cannot be reached using only the allowed moves, print the single word NIE. Otherwise print one integer: the minimum number of moves that reaches the requested final state.