<p>You are given an integer array <code>nums</code> and an integer <code>target</code>.</p>

<p>You want to build an <strong>expression</strong> out of nums by adding one of the symbols <code>&#39;+&#39;</code> and <code>&#39;-&#39;</code> before each integer in nums and then concatenate all the integers.</p>

<ul>
	<li>For example, if <code>nums = [2, 1]</code>, you can add a <code>&#39;+&#39;</code> before <code>2</code> and a <code>&#39;-&#39;</code> before <code>1</code> and concatenate them to build the expression <code>&quot;+2-1&quot;</code>.</li>
</ul>

<p>Return the number of different <strong>expressions</strong> that you can build, which evaluates to <code>target</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [1,1,1,1,1], target = 3
<strong>Output:</strong> 5
<strong>Explanation:</strong> There are 5 ways to assign symbols to make the sum of nums be target 3.
-1 + 1 + 1 + 1 + 1 = 3
+1 - 1 + 1 + 1 + 1 = 3
+1 + 1 - 1 + 1 + 1 = 3
+1 + 1 + 1 - 1 + 1 = 3
+1 + 1 + 1 + 1 - 1 = 3
</pre>

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

<pre>
<strong>Input:</strong> nums = [1], target = 1
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 20</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 1000</code></li>
	<li><code>0 &lt;= sum(nums[i]) &lt;= 1000</code></li>
	<li><code>-1000 &lt;= target &lt;= 1000</code></li>
</ul>

class Solution:
    def findTargetSumWays(self, nums: List[int], target: int) -> int:
        SHIFT = 1000
        dp = [[0] * (2 * SHIFT + 1) for _ in range(len(nums))]
        
        first_num = nums[0]
        # if first_num != 0:?
        dp[0][first_num + SHIFT] += 1
        dp[0][-first_num + SHIFT] += 1

        prev_sums = {first_num, -first_num}

        for i in range(1, len(nums)):
            curr_sums = set()
            num = nums[i]
            for prev_sum in prev_sums:
                dp[i][prev_sum + num + SHIFT] += dp[i - 1][prev_sum + SHIFT]
                dp[i][prev_sum - num + SHIFT] += dp[i - 1][prev_sum + SHIFT]
                curr_sums.add(prev_sum + num)
                curr_sums.add(prev_sum - num)
            prev_sums = curr_sums
            print(dp[i])

        # print(dp)
        return dp[-1][target + SHIFT]
18458