You are given a string $s$ of length $n$ that consists of lowercase English letters. We call a sequence of letters a _word_ if it consists of at least one vowel and at least one consonant. What is the maximum number of words the given string can be partitioned into?
In this problem, we consider the vowels to be the letters _a_, _i_, _o_, _u_, _e_, _y_, and all the other letters are consonants.
The first line of input contains an integer $n$ ($1 <= n <= 10^5$), the length of the string. The next line contains the string $s$ consisting of lowercase English alphabet letters.
Output a single integer, the maximum possible number of words the string can be partitioned into. If it is not possible to partition the string in such a way, output $0$.
## Input
The first line of input contains an integer $n$ ($1 <= n <= 10^5$), the length of the string. The next line contains the string $s$ consisting of lowercase English alphabet letters.
## Output
Output a single integer, the maximum possible number of words the string can be partitioned into. If it is not possible to partition the string in such a way, output $0$.
[samples]
**Definitions**
Let $ n \in \mathbb{Z}^+ $ be the side length of a square matrix $ S \in \{L, R\}^{n \times n} $.
Let $ r $ be the number of cells in $ S $ assigned to 'R'.
**Constraints**
The matrix $ S $ must satisfy the following optimal properties (inferred from example):
- Each row is symmetric: $ S_{i,j} = S_{i,n+1-j} $ for all $ i,j \in \{1,\dots,n\} $.
- Each column is symmetric: $ S_{i,j} = S_{n+1-i,j} $ for all $ i,j \in \{1,\dots,n\} $.
- The center cell (if $ n $ is odd) can be freely assigned.
- The number of 'R' entries is exactly $ k $.
**Objective**
Find the smallest $ n \in \mathbb{Z}^+ $ such that there exists an $ n \times n $ matrix satisfying the above symmetries and containing exactly $ k $ entries equal to 'R'.
**Key Insight**
Due to row and column symmetry, the matrix is determined by its top-left quadrant (including middle row/column if $ n $ is odd).
The number of *independent* cells (i.e., degrees of freedom for assigning 'R') is:
$$
f(n) = \left\lceil \frac{n}{2} \right\rceil \cdot \left\lceil \frac{n+1}{2} \right\rceil
$$
Each independent cell can be set to 'R' or 'L', so the number of 'R's can be any integer from 0 to $ f(n) $.
Thus, we seek the smallest $ n $ such that:
$$
k \leq \left\lceil \frac{n}{2} \right\rceil \cdot \left\lceil \frac{n+1}{2} \right\rceil
$$