<p>You are given a <strong>0-indexed</strong> array <code>nums</code> consisting of <strong>positive</strong> integers.</p>

<p>A partition of an array into one or more <strong>contiguous</strong> subarrays is called <strong>good</strong> if no two subarrays contain the same number.</p>

<p>Return <em>the <strong>total number</strong> of good partitions of </em><code>nums</code>.</p>

<p>Since the answer may be large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4]
<strong>Output:</strong> 8
<strong>Explanation:</strong> The 8 possible good partitions are: ([1], [2], [3], [4]), ([1], [2], [3,4]), ([1], [2,3], [4]), ([1], [2,3,4]), ([1,2], [3], [4]), ([1,2], [3,4]), ([1,2,3], [4]), and ([1,2,3,4]).
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,1,1,1]
<strong>Output:</strong> 1
<strong>Explanation:</strong> The only possible good partition is: ([1,1,1,1]).
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,1,3]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The 2 possible good partitions are: ([1,2,1], [3]) and ([1,2,1,3]).
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def numberOfGoodPartitions(self, nums: List[int]) -> int:
        starts = {}
        ends = {}
        for idx, num in enumerate(nums):
            starts[num] = min(starts.get(num, len(nums)), idx)
            ends[num] = max(ends.get(num, 0), idx)

        intervals = []
        for idx in starts.keys():
            intervals.append((starts[idx], ends[idx]))
        
        intervals = sorted(intervals, key=lambda x:x[0])

        current_interval_start = None
        current_interval_end = None

        dedup_intervals = []
        for start, end in intervals:
            if current_interval_start is None:
                current_interval_start, current_interval_end = start, end
                continue

            if start <= current_interval_end:
                current_interval_end = max(current_interval_end, end)
            else:
                dedup_intervals.append((current_interval_start, current_interval_end))
                current_interval_start, current_interval_end = start, end
        dedup_intervals.append((current_interval_start, current_interval_end))
        k = len(nums) - sum([j - i for i, j in dedup_intervals]) - 1
        
        return 2**(k)  % (10**9 + 7)
56600