Score : $200$ points

Problem Statement

Takahashi is trying to create a game inspired by baseball, but he is having difficulty writing the code. Write a program for Takahashi that solves the following problem.

There are $4$ squares called Square $0$, Square $1$, Square $2$, and Square $3$. Initially, all squares are empty. There is also an integer $P$; initially, $P = 0$. Given a sequence of positive integers $A = (A_1, A_2, \dots, A_N)$, perform the following operations for $i = 1, 2, \dots, N$ in this order:

1. Put a piece on Square $0$.
2. Advance every piece on the squares $A_i$ squares ahead. In other words, if Square $x$ has a piece, move the piece to Square $(x + A_i)$.
   If, however, the destination square does not exist (i.e. $x + A_i$ is greater than or equal to $4$) for a piece, remove it. Add to $P$ the number of pieces that have been removed.

Print the value of $P$ after all the operations have been performed.

Constraints

• $1 \leq N \leq 100$
• $1 \leq A_i \leq 4$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\dots$ $A_N$

Output

Print the value of $P$ after all the operations have been performed.

4
1 1 3 2

3

The operations are described below. After all the operations have been performed, $P$ equals $3$.

• The operations for $i=1$: 1. Put a piece on Square $0$. Now, Square $0$ has a piece. 2. Advance every piece on the squares $1$ square ahead. After these moves, Square $1$ has a piece.
• The operations for $i=2$: 1. Put a piece on Square $0$. Now, Squares $0$ and $1$ have a piece. 2. Advance every piece on the squares $1$ square ahead. After these moves, Squares $1$ and $2$ have a piece.
• The operations for $i=3$: 1. Put a piece on Square $0$. Now, Squares $0$, $1$, and $2$ have a piece. 2. Advance every piece on the squares $3$ squares ahead. Here, for the pieces on Squares $1$ and $2$, the destination squares do not exist (since $1+3=4$ and $2+3=5$), so remove these pieces and add $2$ to $P$. $P$ now equals $2$. After these moves, Square $3$ has a piece.
• The operations for $i=4$: 1. Put a piece on Square $0$. Now, Squares $0$ and $3$ have a piece. 2. Advance every piece on the squares $2$ squares ahead. Here, for the piece on Square $3$, the destination square does not exist (since $3+2=5$), so remove this piece and add $1$ to $P$. $P$ now equals $3$. After these moves, Square $2$ has a piece.

3
1 1 1

0

The value of $P$ may not be updated by the operations.

10
2 2 4 1 1 1 4 2 2 1

8