QQuestionMathematics
QuestionMathematics
Write a "how-many-units-in- 1 -group" word problem for the equation 4÷ 2 / 3 = ?
Use your problem along with a math drawing, table, or double number line to explain why it makes sense to solve 4÷ 2 / 3 by "inverting and multiplying"—in other words, by multiplying 4 by 3 / 2.
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Answer
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Step 1:**Problem:**
A group of friends want to share 4 pizzas equally among themselves. They originally planned to split the pizzas into groups of 2 / 3 of a pizza each, but they realize that this isn't a whole number of pizzas. To make sure everyone gets a fair share, they decide to change the group size. How many units are there in 1 group if they use the "inverting and multiplying" method to solve the problem, 4 ÷ 2 / 3 = 4 × 3 / 2 = 6? **Explanation:**
Step 2:**Visualizing the problem:** Imagine 4 pizzas laid out in a row.
The friends want to divide these into groups of 2 / 3 of a pizza each. However, this isn't possible because 2 / 3 is a fraction, and they can't split a pizza into thirds. ![Pizza Sharing Diagram](data:image/png;base^64,iVBORw^0KGgoAAAANSUhEUgAAAT^4AAACeCAMAAAD^1SvhvAAAAMFBMVEX/// 8AAAD^39 /fm^5ubv^7 +/q^6urqysrK+vr^6dnZ^2ioqK^2trbf^39 /r^6 +vj^4 +P^09PT^29vb^09fX^18fHy^8vL^29vb^29vZ^7VDrhAAAAXklEQVR^4Ae^3U^6Q^3AIAwF^0Jbb/Ri^6UK^5k^5rHzKCGOaWkJSUlJSUlKS^0tLc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nz
Final Answer
The friends want to divide these into groups of 2 / 3 of a pizza each. However, this isn't possible because 2 / 3 is a fraction, and they can't split a pizza into thirds. ![Pizza Sharing Diagram](data:image/png;base^64,iVBORw^0KGgoAAAANSUhEUgAAAT^4AAACeCAMAAAD^1SvhvAAAAMFBMVEX/// 8AAAD^39 /fm^5ubv^7 +/q^6urqysrK+vr^6dnZ^2ioqK^2trbf^39 /r^6 +vj^4 +P^09PT^29vb^09fX^18fHy^8vL^29vb^29vZ^7VDrhAAAAXklEQVR^4Ae^3U^6Q^3AIAwF^0Jbb/Ri^6UK^5k^5rHzKCGOaWkJSUlJSUlKS^0tLc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nzc^3Nz
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