<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) -> int:
        MOD = int(1e9) + 7
        pairs = [[] for _ in range(len(nums))]
        for i in range(len(nums)):
            for j in range(nums[i] + 1):
                pairs[i].append([j, nums[i] - j, 0])
        pairs[0] = [[x[0], x[1], 1] for x in pairs[0]]

        # print(pairs)

        for i in range(1, len(pairs)):
            running = [0] * (max(len(pairs[i]), len(pairs[i - 1])) + 1)
            for j in range(len(pairs[i - 1])):
                index = max(pairs[i - 1][j][0], len(pairs[i]) - pairs[i - 1][j][1] - 1)
                running[index] = (running[index] + pairs[i - 1][j][2]) % MOD

            sum1 = 0
            for j in range(len(pairs[i])):
                sum1 = (sum1 + running[j]) % MOD
                pairs[i][j][2] = (sum1 + pairs[i][j][2]) % MOD

                # for k in range(len(pairs[i])):
                #     if pairs[i][k][0] >= pairs[i - 1][j][0] and pairs[i][k][1] <= pairs[i - 1][j][1]:
                #         pairs[i][k][2] = (pairs[i][k][2] + pairs[i - 1][j][2]) % MOD
        # print(pairs)
        
        return (sum([x[2] for x in pairs[-1]])) % MOD
        
# print(Solution().countOfPairs([2, 3, 2]))
242307