<p>There is a street with <code>n * 2</code> <strong>plots</strong>, where there are <code>n</code> plots on each side of the street. The plots on each side are numbered from <code>1</code> to <code>n</code>. On each plot, a house can be placed.</p>

<p>Return <em>the number of ways houses can be placed such that no two houses are adjacent to each other on the same side of the street</em>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>Note that if a house is placed on the <code>i<sup>th</sup></code> plot on one side of the street, a house can also be placed on the <code>i<sup>th</sup></code> plot on the other side of the street.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 4
<strong>Explanation:</strong> 
Possible arrangements:
1. All plots are empty.
2. A house is placed on one side of the street.
3. A house is placed on the other side of the street.
4. Two houses are placed, one on each side of the street.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/05/12/arrangements.png" style="width: 500px; height: 500px;" />
<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 9
<strong>Explanation:</strong> The 9 possible arrangements are shown in the diagram above.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>
</ul>

import numpy
class Solution:
    def countHousePlacements(self, n: int) -> int:
        # n_plot[i-1] refers to number of ways houses can be placed
        # on each side of street with i plots.
        # We can then place houses in empty series of plots like 
        # either H _ [....] or _[......]
        # which gives definition n_plot[0] = 2, n_plot[1] = 3 n_plot[i] = n_plot[i-1] + n_plot[i-2]
        start = numpy.array([3,2], dtype=int)
        if n <=2:
            return start[2-n]*start[2-n]
        exp = n-2
        matrix = numpy.array([[1,1],[1,0]], dtype=int)
        res = numpy.array([[1,0],[0,1]], dtype=int)
        while exp > 0:
            if exp%2:
                res = (res@matrix)%1000000007
                print("res ", res)
                exp -= 1
            else:
                matrix = (matrix@matrix)%1000000007
                print("matrix ", matrix)
                exp = exp//2
        vval = (res@start)%1000000007
        return (vval[0] * vval[0])%1000000007





        
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