A prison can be represented as a list of cells. Each cell contains exactly one prisoner. A 1 represents an unlocked cell and a 0 represents a locked cell.

[1, 1, 0, 0, 0, 1, 0]

Starting inside the leftmost cell, you are tasked with seeing how many prisoners you can set free, with a catch. You are the prisoner in the first cell. If the first cell is locked, you cannot free anyone. Each time you free a prisoner, the locked cells become unlocked, and the unlocked cells become locked again.

So, if we use the example above:

[1, 1, 0, 0, 0, 1, 0]
# You free the prisoner in the first cell.

[0, 0, 1, 1, 1, 0, 1]
# You free the prisoner in the third cell (2nd one locked).

[1, 1, 0, 0, 0, 1, 0]
# You free the prisoner in the sixth cell (3rd, 4th and 5th locked).

[0, 0, 1, 1, 1, 0, 1]
# You free the prisoner in the seventh cell - and you are done!

Here, we have set free 4 prisoners in total.

Create a function that, given this unique prison arrangement, returns the number of freed prisoners.

Examples

freed_prisoners([1, 1, 0, 0, 0, 1, 0]) ➞ 4

freed_prisoners([1, 1, 1]) ➞ 1

freed_prisoners([0, 0, 0]) ➞ 0

freed_prisoners([0, 1, 1, 1]) ➞ 0

Notes

• You are the prisoner in the first cell. You must be freed to free anyone else.
• You must free a prisoner in order for the locks to switch. So in the second example where the input is [1, 1, 1] after you release the first prisoner, the locks change to [0, 0, 0]. Since all cells are locked, you can release no more prisoners.
• You always start with the leftmost element in the list (the first prison cell). If all the prison cells to your right are zeroes, you cannot free any more prisoners.