Problem Statement

A random walk generally refers to a motion in which the next position is determined randomly.
Here, consider the following random walk of a point P on a number line.
・At time $t=0$, point P is at the origin.
・When P is at coordinate $x$ at some time $t$, at time $(t+1)$ it moves to coordinate $(x+1)$ with probability $\frac{1}{2}$ and to coordinate $(x-1)$ with probability $\frac{1}{2}$.
You are given a sequence $X_i$ of length $T$. Determine whether this sequence can be a record, in order, of the coordinates of point P from time $1$ to time $T$.

Input

T
X_1
X_2
...
X_T

$1 \le T \le 100$
$-100 \le X_i \le 100$
The first line contains the length $T$ of the sequence.
Each of the following $T$ lines contains the coordinate $X_i$ of P at time $i$.

Output

Print "T" if the sequence $X_i$ can be a record, in order, of the coordinates of point P, and "F" otherwise.
Print a newline at the end.

Sample

3
1
2
1

T

5
-1
-2
0
1
2

F

4
0
1
2
1

F