Simple example but Excel Solver can't find feasible solution

I want to make a travel plan using Excel Solver to decide which city to visit in order and how long to stay.
I'm going to leave from city A and come back to city A.

Below table shows the airfare for moving from one city to another, and the cost of accommodation per day for staying in each city.
aa.PNG

Target(Blue cell): To minimize Total expense (N17)
Cells to change(Green cells): Staying days in a city ($D$17:$F$19)

For example, 9 in F17 cell means moving from A to C and staying in C for 9 days.
'From count'(Column H) checks the number of departures from each city
=COUNTIF(D18:G18,">0")

'To count'(Row 22) checks number of times you arrive in each city
=COUNTIF(D18:D21,">0")

'necessary?'(Column K) checks if you have ever arrived in the city (because if you have arrived, you also have to leave)
=HLOOKUP(C19,$D$17:$G$22,6,FALSE)

Constraints include following
-- We're not moving to the same city
> D18 = 0
> E19 = 0
> F20 = 0
> G21 = 0
-- Number of staying should be an integer
D18:G21 = integer
-- travel starts from city A
H18 = 1
-- come back to city A
D22 = 1
-- We're not going to stop by a city more than once
> H19:H21 <= 1
> E22:G22 <= 1
-- if you have arrived in a city, you also have to leave
> H19:H21 >= K19:K21
-- Total staying days (except to come back to A and stay) should be 10
> D26 = sum(E18:G21) = 10
-- Total visiting cities (except A) should be 2
> D27 = sum(E22:G22) = 2
-- Number of days to return to A and stay at A is randomly specified as 1
> D19:D21 <= 1

I think the number shown on the screen would be the best travel plan. If I enter this number and run solver, I find a solution, but if I clear all the numbers and run it, I don't find a solution.

I'd like to use this logic in five city examples, but Excel can't find a feasible solution even in this toy example.

What's the reason and how can I make it work?

I have attached the related Excel file.

*I heard that solver does not recognize countif function, so I tried to use iferror, for example, in cell H18
=IFERROR(D18/D18, 0)+IFERROR(E18/E18, 0)+IFERROR(F18/F18, 0)+IFERROR(G18/G18, 0)
instead of countif, but I also couldn't find a solution.

sample_problem.xlsx

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