A rectangle in the Cartesian plane is speci ed by a pair of coordinates (x1 , y1) and (x2 , y2) indicating its lower-left and upper-right corners, respectively (where x1 ≤ x2 and y1 ≤ y2). Given a pair of rectangles,A = ((x ^A ₁ , y ^A ₁ ), (x ^A ₂ ,y ^A ₂ )) and B = ((x ^B ₁ , y ^B ₁ ), (x ^B ₂ , y ^B ₂ )), we write A ≤ B (i.e., A "precedes" B), if x ^A ₂ < x ^B ₁ and y ^A ₂ < y ^B ₁ :In this problem, you are given a collection of rectangles located in the two-dimension Euclidean plane. Find the length L of the longest sequence of rectangles (A ₁,A ₂,…,A _L) from this collection such that A ₁ ≤ A ₂ ≤ … ≤ A _L.

The input fi le will contain multiple test cases. Each test case will begin with a line containing a single integer n (where 1 ≤ n ≤ 100000), indicating the number of input rectangles. The next n lines each contain four integers x ⁱ ₁ ,y ⁱ ₁ ,x ⁱ ₂ ,y ⁱ ₂ (where -1000000 ≤ x ⁱ ₁ ≤ x ⁱ ₂ ≤ 1000000, -1000000 ≤ y ⁱ ₁ ≤ y ⁱ ₂ ≤ 1000000, and 1 ≤ i ≤ n), indicating the lower left and upper right corners of a rectangle. The end-of-file is denoted by asingle line containing the integer 0.

For each input test case, print a single integer indicating the length of the longest chain.