Problem Statement

MKM has a grid-shaped stamp of length $N$. Each cell of the stamp has paint on it. The color of the paint on the $i$-th cell is $a_i$.

MKM also has a grid-shaped sheet of paper of length $2 \times N-1$. Initially, none of its cells has any paint on it.

MKM presses the stamp on the paper several times. This information is given as a sequence $b_i$ of length $N$. Each $b_i$ is $0$ or $1$, and $1$ means that he pressed the stamp so that its left end overlapped the $i$-th cell from the left of the paper. He never presses the stamp at the same position $2$ times.

For each cell, MKM wants to count how many colors of paint are mixed in it. However, this turned out to be difficult, so for now he decided to determine only whether the answer is even or odd.

Note that the paper is dried after every press of the stamp, so you do not need to consider paint on the paper transferring to the stamp.

Input

$N$
$a_1$ $a_2$ $\dots$ $a_N$
$b_1$ $b_2$ $\dots$ $b_N$

All inputs are integers.

$1 \le N \le 100,000$
$1 \le a_i \le 100,000$
$b_i$ is $0$ or $1$

Output

Output $2 \times N-1$ lines.
On the $i$-th line, print "EVEN" if the answer for the $i$-th cell is even, and "ODD" if it is odd.

Sample

3
1 2 3
1 0 1

ODD
ODD
EVEN
ODD
ODD

3
1 2 1
1 0 1

ODD
ODD
ODD
ODD
ODD