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# Minimum Falling Path Sum II

Given a square grid of integers `arr`, a *falling path with non-zero shifts* is a choice of exactly one element from each row of `arr`, such that no two elements chosen in adjacent rows are in the same column.

Return the minimum sum of a falling path with non-zero shifts.

**Example 1:**

```
Input: arr = [[1,2,3],[4,5,6],[7,8,9]]
Output: 13
Explanation: 
The possible falling paths are:
[1,5,9], [1,5,7], [1,6,7], [1,6,8],
[2,4,8], [2,4,9], [2,6,7], [2,6,8],
[3,4,8], [3,4,9], [3,5,7], [3,5,9]
The falling path with the smallest sum is [1,5,7], so the answer is 13.
```

**Constraints:**

* `1 <= arr.length == arr[i].length <= 200`
* `-99 <= arr[i][j] <= 99`

```java
class Solution {
    public int minFallingPathSum(int[][] arr) {
        // Bottom up approach
        int minSum = Integer.MAX_VALUE, secondMinSum = Integer.MAX_VALUE;
        int index = -1;
        // Find 2 smallest sum path sum in each level
        for (int i = arr.length - 1; i >= 0; i--) {
            int tempSmall = Integer.MAX_VALUE, tempSecondSmall = Integer.MAX_VALUE;
            int t = -1;
            for (int j = 0; j < arr[i].length; j++) {
                int currentSum = arr[i][j];
                if (i != arr.length - 1) {
                    if (j != index)
                        currentSum += minSum;
                    else
                        currentSum += secondMinSum;
                }
                if (currentSum < tempSmall) {
                    tempSecondSmall = tempSmall;
                    tempSmall = currentSum;
                    t = j;
                } else if (currentSum < tempSecondSmall)
                    tempSecondSmall = currentSum;
            }
            minSum = tempSmall;
            secondMinSum = tempSecondSmall;
            index = t;
        }
        return minSum;
    }
}
```


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