Olivander's wand boxes

Given N wand lengths and N box sizes, decide whether every wand can be paired with a distinct box whose size is at least the wand length.

Easy3SortingGreedyTwo pointersArrayInterviewNo attempts yetTime limit1sMemory limit64 MB

Problem

Harry Potter broke his wand while fighting Voldemort, so he decided to buy a new one at Olivander's wand shop. On the shop floor lie NN wands and NN wand boxes. The wand lengths are X1,X2,,XNX_1, X_2, \dots, X_N and the box sizes are Y1,Y2,,YNY_1, Y_2, \dots, Y_N.

A wand of length XX can go into a box of size YY if XYX \le Y. Harry wants to know whether he can put all NN wands away so that each box holds exactly one wand. Help him decide.

Input

The first line contains NN, the number of wands and boxes. (1N1001 \le N \le 100)

The second line contains the wand lengths X1,X2,,XNX_1, X_2, \dots, X_N, separated by spaces. (1Xi1091 \le X_i \le 10^9)

The third line contains the box sizes Y1,Y2,,YNY_1, Y_2, \dots, Y_N, separated by spaces. (1Yi1091 \le Y_i \le 10^9)

Output

Print DA if Harry can put every wand into a box, and NE otherwise. DA and NE are Croatian for yes and no.

Hint

In the first example every wand fits. Harry can put the wand of length 5 into the box of size 6, the wand of length 7 into the box of size 13, and the wand of length 9 into the box of size 10.

In the second example no wand fits into the box of size 2, so he cannot put all of them away.