Please modify this function in Python. It is a Futoshiki solver that is similar to Latin Squares, but just needs a modification to the solver method.

Here is the code:

def is$\_$valid$($board$,$ row, col, num$)$:

N $=$ len$($board$)$

# Check if the number is not in the same row and column

if num in board$[$row$]$ or num in $[$board$[$i$][$col$]$ for i in range$(4)]$:

return False

# Check inequality constraints

inequality$\_$signs $=[\text{'}<\text{'},\text{'}>\text{'},\text{'}^\text{'},\text{'}$v$\text{'}]$

for sign in inequality$\_$signs:

if sign $==\text{'}<\text{'}$:

if col $>0$ and board$[$row$][$col $-1]==$ num:

return False

elif sign $==\text{'}>\text{'}$:

if col $<$ N $-1$ and board$[$row$][$col $+1]==$ num:

return False

elif sign $==\text{'}^\text{'}$:

if row $>0$ and board$[$row $-1][$col$]==$ num:

return False

elif sign $==\text{'}$v$\text{'}$:

if row $<$ N $-1$ and board$[$row $+1][$col$]==$ num:

return False

return True

def solve$\_$futoshiki$($board$)$:

empty $=$ find$\_$empty$\_$location$($board$)$

if not empty:

return True # Puzzle solved

row, col $=$ empty

for num in range$(1,5)$: # Numbers $1$ to $4$ in a $4$x$4$ grid

if is$\_$valid$($board$,$ row, col, num$)$:

board$[$row$][$col$]=$ num

if solve$\_$futoshiki$($board$)$:

return True # If solution is found, return True

board$[$row$][$col$]=0$ # Backtrack if the current configuration does not lead to a solution

return False

The output should be:

$[2,1,4,3]$

$[3,1,4,2]$

$[4,3,1,2]$

$[2,1,3,1]$

But right now my output is:

$[1,2,3,4]$

$[2,1,4,3]$

$[3,4,1,2]$

$[4,3,2,1]$