As we all know, the girls in the anime are always high school students and also need to go to school every day. So, hanging a piece of bread in their mouth haste to school is always a stereotype. 

But things always go bad sometimes, just like went to bed late last night and had to go to school in time, or just have to go to some retails to buy something. So, the shortest way to school is some time not an optimal way. In this case, we need to find one way which exactly contains k steps and each step will not overlap with each other (overlap means we can’t go to the same route twice). Just as below, we can’t go back to A from B, because we have gone through this route before. 

And for some simplification, we can imagine that the block is just like a matrix and we have to go to school in just k steps from our house. And your house is on the up left and the school is on the bottom right.

One optional way from our house to school in 9 steps is just EEEEESSSS 

And one optional way from our house to school in 11 steps is just EEEEESSSWSE 

So, give you a 𝑛 × 𝑚 block and the number 𝑘, can you find one way from your house to school within exact k steps and each step will not overlap with each other? 

输入描述:

The first line of input contains one integer 𝑇( 1 ≤ 𝑇 ≤ 1000), indicates the number of testcases. 
Then followed 𝑇 lines each line contains three integers, 𝑛, 𝑚, 𝑘( 1 ≤ 𝑛, 𝑚 ≤ 1000, 1 ≤𝑘 ≤  ). 

输出描述:

For each test case, if there exists one k-th route, print YES and on the other line print theexact route using N(north) S(south) E(east) W(west). 
If there are multiple solutions just print any. 
If there doesn’t exist one route, just print NO. 
It Is guaranteed that the length of all the routes which need to be output doesn't exeed .

1
2 3 4

NO

We have more testcases like:
2
2 2 4
3 4 9

YES
EESS
YES
EEESSWSEE

For the second testcase: