Find the shortest distance from S to E on the network below. $[40]$

The cost between node S and node A is $-1$st number of your student number.

The cost between node A and node B is $-2$nd number of your student number.

The cost between node A and node C is $-3$rd number of your student number.

The cost between node B and node D is $-4$th number of your student number.

The cost between node S and node B is $-5$th number of your student number.

The cost between node C and node D is $-6$th number of your student number.

The cost between node C and node E is $-7$th number of your student number.

The cost between node D and node E is $-8$th number of your student number.

The cost between node A and node D is $-9$th number of your student number.

If there is a $0$ in your student number change it to $1$ i$.$e if your student number is $215412807$ use it as $215412817.$ If there are repeating numbers like $218264666$ change it to $218264657$ or $218264678$ i$.$e add or subtract $1.$ Don$$t use a number more than twice. If you still have number repeated more than twice add$/$subtract $2$ or $3$ to the number to make it different.