Due to the success of TWICE, JYP Entertainment has earned countless money and emerged as the biggest entertainment firm by market capitalization. Therefore, the boss, JYP, has decided to create a new nation and has appointed you to provide a design diagram.

The new nation consists of $n$ cities and some roads between them. JYP has given some restrictions:

• To guarantee efficiency while avoiding chaos, for any $2$ different cities $A$ and $B$, there is exactly one road between them, and it is one-directional. There are no roads connecting a city to itself.

• The logo of rivaling companies should not appear in the plan, that is, there does not exist $4$ distinct cities $A$,$B$,$C$,$D$ , such that the following configuration occurs.

JYP has given criteria for your diagram. For two cities $A$,$B$, let $dis(A,B)$ be the smallest number of roads you have to go through to get from $A$ to $B$. If it is not possible to walk from $A$ to $B$, $dis(A,B) = 614n$. Then, the efficiency value is defined to be the sum of $dis(A,B)$ for all ordered pairs of distinct cities $(A,B)$.

Note that $dis(A,B)$ doesn't have to be equal to $dis(B,A)$.

You have drawn a design diagram that satisfies JYP's restrictions. Find the sum of $dis(A,B)$ over all ordered pairs of cities $(A,B)$ with $A\neq B$.

Note that the input is given in compressed form. But even though it is compressed, you'd better use fast input.

The first line contains a single integer $n$ ($4 \le n \le 8000$, $n \equiv 0 \pmod{4}$) — the number of cities.

A binary matrix is encrypted in the following format. Each of $n$ next lines contains $\frac{n}{4}$ one-digit hexadecimal numbers (that is, these numbers can be represented either as digits from $0$ to $9$ or as uppercase Latin letters from $A$ to $F$). Binary representation of each of these numbers denotes next $4$ elements of the matrix in the corresponding row. For example, if the number $B$ is given, then the corresponding elements are $1011$, and if the number is $5$, then the corresponding elements are $0101$.

After you obtain the decrypted binary matrix, the $j$-th character of the $i$-th row is $1$ if the one-directional road between cities $i$ and $j$ is directed from $i$ to $j$, and $0$ otherwise. It is guaranteed that the graph satisfies the restrictions mentioned above.

Output one integer, representing the sum of $dis(A,B)$ over all ordered pairs of cities $(A,B)$ with $A\neq B$.