The Hypercube Hotel game is also very popular and universally acclaimed. Get it for the Phillips CD-i while it lasts!

The Hypercube Hotel is a strange new mathematically themed hotel, a competitor to Hilbert's Hotel. The hotel has an unusual way of numbering its rooms. Each room has an $N$ digit number so that the $i^{\text{th}}$ digit (from the left) is between $1$ and $A_i$. Conversely, every number in this form has a corresponding room. Room numbers are unique.

Two different rooms are called neighbours if for every $i$, the $i^{\text{th}}$ digit of the two room numbers differ by at most $1$. For example, the rooms with numbers $213$ and $222$ are neighbours but the rooms with numbers $111$ and $131$ are not neighbours. A room is not a neighbour of itself.

All the rooms in the hotel are occupied, so each room generates a certain amount of noise. If a room has number $m$, call this quantity $x_m$. For each room, the noise level of that room is the sum of the amounts of noise generated by its neighbours. Given the amount of noise generated by each room, find the noise level of each room.

Constraints

$1\le N\le 9$

$1\le A_i\le 5$

$0\le x_m\le {10}^{14}$

Subtask	Points	Additional Constraints
1	5	$N=2$
2	5	$A_i\le 2$
3	5	$N\le 5$, $A_i\le 4$, $x_m\le 100$
4	15	$N\le 7$, $A_i\le 4$, $x_m\le 100$
5	70	None

Input Specification

The first line contains the integer $N$.

The next line contains $N$ integers $A_1,A_2,\dots ,A_N$.

The next $A_1\times A_2\times \cdots \times A_N$ lines each contain a single integer $x_m$. The lines are given in increasing order of the room number $m$.

Output Specification

For each room, output a line containing a single integer, the noise level of that room. Do this in increasing order of room number.

Sample Input

2
2 3
1
2
3
4
5
6

Sample Output

11
19
13
8
16
10