So as we just covered by hand the calculation from the forward and the backward past calculations, I'm also highlighting here, as you would see just quickly, we'll not go through in details. Because we just did on that node early, the earliest time to start in that node and the earliest start dates and to highlight here how we find the early finish dates for activity A, and activity B here, as you can see the numbers 3 and 2. And then we move forward with the numbers 4, 3, and 2, and we calculate all the early start and the early finish dates with the earliest time a node can reach one activity on arrow and find the duration of the project 15 minus one of our schedule here. The same we did for the backward pass calculations which we start similar to what we did from the activity on node before, which we have the same number, 15, and we take that number backward as we can see here. But I left all the numbers in red on the top of all the arrows as we highlighted before on the key, on what is the early start and the early finish of each activity just to compare. And we go backward as we can see here, 15 minus 1 to find the late start of activity J, and then to identify the latest time to reach each node in our project. Do all the calculations backward until we reach that same node we have for the first node. And then I popped up, A question here about the critical path, which highlights what would be our critical path for this project. The easiest way to highlight would be two quick things. One, what's the longest duration from all the activities or possible sequence activities from the start towards the end of the project? For me I also, of course, look at the early start and the late start to be equal as well as the early finish and the late finish of all the activities. So I highlight here in yellow, what would be my critical path of my project, and if you add the duration that has an obvious activities, it will also reach the duration that we found towards the end of 14 days of the project that we have here in the schedule. So, that being said, I would love to wrap this activity on arrow diagram that we just covered to compare it with what we did in activity on node before. And I highlighted four points that you need to understand is activity on node is kind of a little better than activity on arrow 4 for several reasons, 1, it is much easier to construct and to modify as well as to draw than an activity on arrow. Second, if you would think about it, we just introduced to you what is Dummy activities. An activity on node, we do not use any Dummy activities in our diagrams. So we just go through the relationships right away from a node to the relationship in the arrow to the other node at the end which represent the activity itself. Activity and node accommodates also Lags that I give several examples. And that helps us to reduce actually the number of activities because sometimes in the activity on arrow, you do need to introduce another arrow with two nodes to highlight that lag duration that you need to wait until the activity finishes. Couple of the examples we give in the previous modules, related to waiting for the concrete to cure before you take out the forms. Last but not least, activity on node has the ability to show more types of relationship. As we explained, the precedence diagram and it highlights four kinds of relationships with the three that I focus on that are more common in our construction industry, which is a finish to stop relationship, start to start, and finish to finish. We have the multiple and the start to finish but rarely you can find them in our industry. With all that, I summarize it is to have the Lag, to have the ability to show more relationships because an activity on arrow, the only thing you show is the finish to start relationship. With that it will give you less activities when you're presenting or when there are presentations of all the list of activities you have in the project. So that is also tremendous kind of benefit to use an activity on node versus an activity on arrow. More over, I also highlighted after we finish the activity on nodes and activity on arrows, which is in network diagrams, to that bar charts or Gantt charts that we covered early in the course. And the three basic ones that I'd like to share with you here is the network diagrams show the logic between the construction activities. As I explained, bar charts do not show that logic, unless you start to put some arrows within it, which will make it very complicated and sometimes look like spaghetti kind of thing which is really messy. So I do not recommend that and when it comes to show logic and also for the networks it's better especially activity on nodes representation of larger projects than the bar charts. Last but not least networks can estimate and predict and calculate that completion date of your project, and early start early finish, let's start let's finish, to identify the critical path, when you do the critical path calculations, and to identify the floats, and so on. But bar charts don't have this ability to do this kind of calculations and estimations. However, I'm not going to go through it here, but if you go back in module about bar charts still, we have very good use why we need bar charts and the benefits of using them despite these constraints. With that we finalize the activity on Arrow and thank you for watching this module.