Hamburger

Interview

Time limit1sMemory limit1024 MB

Summary

Given a string S of bread, patty, lettuce, and tomato, check whether it is a valid hamburger: bread at both ends, no equal neighbors, and counts within A, B, C, D.

Level: Easy2 of 10
Topics: String, Implementation
Solved: No attempts yet

Problem

haru_101 has $A$ pieces of bread, $B$ patties, $C$ lettuce leaves, and $D$ tomato slices, all of the same kind. Stack the ingredients under the following rules, and call the result a tasty hamburger.

Stack the ingredients from bottom to top.
The bottom ingredient and the top ingredient must both be bread.
Two adjacent ingredients cannot be the same.
Not every ingredient has to be used, but the hamburger must be made only from the ingredients on hand.

haru_101 wrote the hamburger to make as a string $S$ . Write a program that determines whether this hamburger is a tasty hamburger.

Input

The first line contains the length $N$ of the string $S$ .

The second line contains the integers $A$ , $B$ , $C$ , and $D$ , separated by spaces.

The third line contains the string $S$ , which consists only of the lowercase letters a, b, c, and d. The leftmost character of $S$ is the bottom ingredient, and the rightmost character is the top ingredient. a is bread, b is a patty, c is lettuce, and d is a tomato.

Output

Print Yes if the hamburger made from $S$ is a tasty hamburger. Otherwise, print No.

Constraints

$1 \leq N \leq 100\,000$
$1 \leq A+B+C+D \leq 100\,000$
$A$ , $B$ , $C$ , and $D$ are non-negative integers

Examples2

Example 1
Input
```
5
2 1 1 1
abdca
```
Expected output
```
Yes
```
Example 2
Input
```
2
2 2 1 0
aa
```
Expected output
```
No
```