please help fix my pyomo code to solve my sudoku problem i almost have it but my output is giving me the wrong values:import pyomo.environ as pyo

# Define the model and grid parameters

model $=$ pyo.ConcreteModel$()$

N $=9$ # Grid size for standard Sudoku

values$\_$range $=$ range$(1,$ N $+1)$

rows$\_$range $=$ range$($N$)$

cols$\_$range $=$ range$($N$)$

# Decision variable: x$[$r$,$ c$,$ n$]$ is $1$ if number n is in cell $($r$,$ c$),0$ otherwise

model.x $=$ pyo.Var$($rows$\_$range, cols$\_$range, values$\_$range, domain$=$pyo.Binary$)$

model.constraints $=$ pyo.ConstraintList$()$

# Constraint $1$: Each cell contains exactly one number

for r in rows$\_$range:

for c in cols$\_$range:

model.constraints.add$($sum$($model$.$x$[$r$,$ c$,$ n$]$ for n in values$\_$range$)==1)$

# Constraint $2$: Each number appears exactly once in each row

for r in rows$\_$range:

for n in values$\_$range:

model.constraints.add$($sum$($model$.$x$[$r$,$ c$,$ n$]$ for c in cols$\_$range$)==1)$

# Constraint $3$: Each number appears exactly once in each column

for c in cols$\_$range:

for n in values$\_$range:

model.constraints.add$($sum$($model$.$x$[$r$,$ c$,$ n$]$ for r in rows$\_$range$)==1)$

# Constraint $4$: Each number appears exactly once in each $3$x$3$ block

sqrtN $=3$

for n in values$\_$range:

for br in range$(0,$ N$,$ sqrtN$)$:

for bc in range$(0,$ N$,$ sqrtN$)$:

model.constraints.add$($

sum$($model$.$x$[$br $+$ j$,$ bc $+$ i$,$ n$]$

for i in range$($sqrtN$)$

for j in range$($sqrtN$)$

$)==1$

$)$

# Constraint $5$: Pre$-$filled cells

prefilled$\_$cells $=\{$

$(0,0,8),(1,2,3),(1,3,6),$

$(2,1,7),(2,4,9),(2,6,2),$

$(3,0,1),(3,1,5),(3,5,7),$

$(4,4,4),(4,5,5),(4,6,7),$

$(5,3,1),(5,7,3),$

$(6,3,9),(6,7,6),(6,8,8),$

$(7,2,8),(7,3,5),(7,7,1),$

$(8,1,9),(8,6,4)$

$\}$

# Enforce pre$-$filled cells by setting the specific cell variables to $1$

for $($r$,$ c$,$ n$)$ in prefilled$\_$cells:

model.constraints.add$($model$.$x$[$r$,$ c$,$ n$]==1)$

# Objective function $($no specific objective, just find a feasible solution$)$

model.obj $=$ pyo.Objective$($expr$=0,$ sense$=$pyo.maximize$)$

# Solve the model

solver $=$ pyo.SolverFactory$("$glpk$")$

result $=$ solver.solve$($model$,$ tee$=$True$)$

# Output the solved values for only the missing cells, ordered from $(0,1)$ to $(8,8)$

if result.solver.termination$\_$condition $==$ pyo.TerminationCondition.optimal:

print$("$Solved Sudoku Puzzle $($only missing cells$)$:$")$

for r in rows$\_$range:

for c in cols$\_$range:

for n in values$\_$range:

# Print only missing cells, skip prefilled

if model.x$[$r$,$ c$,$ n$].$value $==1$ and $($r$,$ c$,$ n$)$ not in prefilled$\_$cells:

print$($f$"(\{$r$\},\{$c$\},\{$n$\})")$

else:

print$("$No optimal solution found. Solver termination condition:", result.solver.termination$\_$condition$)$

MY OUTPUT:runfile$(\text{'}$C:$/$Users$/$eddy$\_/$untitled$12.$py$\text{'},$ wdir$=\text{'}$C:$/$Users$/$eddy$\_\text{'})$ GLPSOL: GLPK LP$/$MIP Solver, v$4\mathrm{.}65$ Parameter$($s$)$ specified in the command line: $--$write C:$\backslash$Users$\backslash$eddy$\_\backslash$AppData$\backslash$Local$\backslash$Temp$\backslash$tmpwl$93$mk$5$o$.$glpk$.$raw $--$wglp C:$\backslash$Users$\backslash$eddy$\_\backslash$AppData$\backslash$Local$\backslash$Temp$\backslash$tmppwj$677$jm$.$glpk$.$glp $--$cpxlp C:$\backslash$Users$\backslash$eddy$\_\backslash$AppData$\backslash$Local$\backslash$Temp$\backslash$tmppbshezic$.$pyomo.lp Reading problem data from $\text{'}$C:$\backslash$Users$\backslash$eddy$\_\backslash$AppData$\backslash$Local$\backslash$Temp$\backslash$tmppbshezic$.$pyomo.lp$\text{'}...$ C:$\backslash$Users$\backslash$eddy$\_\backslash$AppData$\backslash$Local$\backslash$Temp$\backslash$tmppbshezic$.$pyomo.lp:$4717$: warning: lower bound of variable $\text{'}$x$4\text{'}$ redefined C:$\backslash$Users$\backslash$eddy$\_\backslash$AppData$\backslash$Local$\backslash$Temp$\backslash$tmppbshezic$.$pyomo.lp:$4717$: warning: upper bound of variable $\text{'}$x$4\text{'}$ redefined $346$ rows, $730$ columns, $2938$ non$-$zeros $729$ integer variables, all of which are binary $5446$ lines were read Writing problem data to $\text{'}$C:$\backslash$Users$\backslash$eddy$\_\backslash$AppData$\backslash$Local$\backslash$Temp$\backslash$tmppwj$677$jm$.$glpk$.$glp$\text{'}...4364$ lines were written GLPK Integer Optimizer, v$4\mathrm{.}65346$ rows, $730$ columns, $2938$ non$-$zeros $729$ integer variables, all of which are binary Preprocessing... $228$ rows, $228$ columns, $912$ non$-$zeros $228$ integer variables, all of which are binary Scaling... A: min$|$aij$|=1\mathrm{.}000$e$+00$ max$|$aij$|=1\mathrm{.}000$e$+00$ ratio $=1\mathrm{.}000$e$+00$ Problem data seem to be well scaled Constructing initial basis... Size of triangular part is $155$ Solving LP relaxation... GLPK Simplex Optimizer, v$4\mathrm{.}65228$ rows, $228$ columns, $912$ non$-$zeros $0$: obj $=-0\mathrm{.}000000000$e$+00$ inf $=5\mathrm{.}400$e$+01(40)58$: obj $=-0\mathrm{.}000000000$e$+00$ inf $=4\mathrm{.}554$e$-14(0)$ OPTIMAL LP SOLUTION FOUND Integer optimization begins... Long$-$step dual simplex will be used $+58$: mip $=$ not found yet $<=+$inf $(1$; $0)+102$: $>>>>>0\mathrm{.}000000000$e$+00<=0\mathrm{.}000000000$e$+000\mathrm{.}0\%(4$; $0)+102$: mip $=0\mathrm{.}000000000$e$+00<=$ tree is empty $0\mathrm{.}0\%(0$; $7)$ INTEGER OPTIMAL SOLUTION FOUND Time used: $0\mathrm{.}0$ secs Memory used: $0\mathrm{.}7$ Mb $(747476$ bytes$)$ Writing MIP solution to $\text{'}$C:$\backslash$Users$\backslash$eddy$\_\backslash$AppData$\backslash$Local$\backslash$Temp$\backslash$tmpwl$93$mk$5$o$.$glpk$.$raw'... $1085$ lines were written Solved Sudoku Puzzle $($only missing cells$)$: