<p>You are given an array of <strong>positive</strong> integers <code>nums</code> of length <code>n</code>.</p>

<p>We call a pair of <strong>non-negative</strong> integer arrays <code>(arr1, arr2)</code> <strong>monotonic</strong> if:</p>

<ul>
	<li>The lengths of both arrays are <code>n</code>.</li>
	<li><code>arr1</code> is monotonically <strong>non-decreasing</strong>, in other words, <code>arr1[0] &lt;= arr1[1] &lt;= ... &lt;= arr1[n - 1]</code>.</li>
	<li><code>arr2</code> is monotonically <strong>non-increasing</strong>, in other words, <code>arr2[0] &gt;= arr2[1] &gt;= ... &gt;= arr2[n - 1]</code>.</li>
	<li><code>arr1[i] + arr2[i] == nums[i]</code> for all <code>0 &lt;= i &lt;= n - 1</code>.</li>
</ul>

<p>Return the count of <strong>monotonic</strong> pairs.</p>

<p>Since the answer may be very 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>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [2,3,2]</span></p>

<p><strong>Output:</strong> <span class="example-io">4</span></p>

<p><strong>Explanation:</strong></p>

<p>The good pairs are:</p>

<ol>
	<li><code>([0, 1, 1], [2, 2, 1])</code></li>
	<li><code>([0, 1, 2], [2, 2, 0])</code></li>
	<li><code>([0, 2, 2], [2, 1, 0])</code></li>
	<li><code>([1, 2, 2], [1, 1, 0])</code></li>
</ol>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [5,5,5,5]</span></p>

<p><strong>Output:</strong> <span class="example-io">126</span></p>
</div>

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

<ul>
	<li><code>1 &lt;= n == nums.length &lt;= 2000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>
</ul>

class Solution:
    def countOfPairs(self, nums: List[int]) -> int:
        n = len(nums)
        if n == 1:
            return nums[0] + 1
        max_num = max(nums)
        prev_min = []
        min_num = math.inf
        for i, num in enumerate(nums):
            if num <= min_num:
                prev_min.append(min_num)
                min_num = num
            else:
                prev_min.append(min_num)

        mod = 10**9 + 7
        dp = [[0] * n for _ in range(max_num + 1)]
        for i in range(nums[n-1]+1):
            dp[i][n-1] = 1
        #print(dp)
        prev_sum = nums[n-1] + 1
        for j in range(n - 2, -1, -1):
            curr_sum = 0
            next_num = 0
            for num in range(nums[j] + 1):
                #check left if still possible
                while next_num < num or nums[j] - num < nums[j+1] - next_num:
                    prev_sum -= dp[next_num][j+1]
                    next_num += 1
                if nums[j] - num <= prev_min[j]:
                    dp[num][j] = prev_sum
                    curr_sum += prev_sum
                #prev_sum -= dp[num][j+1]
            prev_sum = curr_sum
            #print(dp)
        return prev_sum % mod
252237