Consonant Chronicles

In the heart of ICPC's code-filled realm, you encountered a cryptic two-dimensional character array consisting of lowercase latin letters. But, here's the twist: vowels $(a, e, i, o, u)$ were ignored to create a labyrinth of consonants. As you navigate through this labyrinth using the directions (left, right, up, and down) provided, you'll collect characters to create a secret message. After decoding this message, you'll face a set of thrilling word challenges.

There are two key steps to your quest:

1. $Array Navigation$: Your journey starts at the top-left cell $(0,0)$, where you'll follow the given directions $(l-left, r-right, u-up, d-down)$ in sequence. During your journey, you must record the characters you collect while ignoring Vowels. Your objective is to display the string after navigating the array.

2. $Query Handling$: After you've collected a sequence of characters using $Array Navigation$, you'll receive a series of word queries. Your mission is to determine if each query word can be formed using the collected characters while preserving their order. That means if you pick a character from $i^{th}$ index of the navigated string to form a query word, you can not pick a character from the lower index anymore.

Input

First line of the test case contains four integers: $n, m, l$ and $q$ representing the array dimensions, length of the string of valid direction and the number of queries separated by spaces.

Each of the next $n$ lines contains a string of $m$ characters consist of lowercase latin letters.

The next line contains the string $S_d$ of valid directions for $Array Navigation$.

Finally, each of the next $q$ lines contains a query string $S_q$ consist of lowercase latin letters.

$1 ≤ n, m, l, q ≤ 10^3$

$S_d$$=$ {$l, r, u, d$}

$1≤ S_q ≤ 10^3$

Output

First line of the output contains a single string formed by $Array Navigation$.

For each of the next $q$ lines, print "YES" if the query string can be formed using $Query Handling$ and "NO" otherwise without quotations.

Samples

Input	Output
3 3 6 2 aei ouk btc rrdldl bk kb	ktb NO YES
Word $bk$ can not be formed because, after picking character $b$ you can not pick $k$ as it is situated in lower index. Word $kb$ can be formed because, first you can pick $k$ and then you can pick $b$ from higher index.

Input	Output
4 4 11 3 rnst xiue aorp bzei dudrurrddlu p noise str	rxrxnstpr YES NO YES