## Goal

There are three frogs sitting on a two-dimensional plane. The ith frog starts at coordinates `xi`, `yi`. Whenever the ith frog jumps, it jumps in such a way that each of its coordinates either remains unchanged or it changes by exactly `ki`. If all three frogs can eventually meet at the same coordinates, print "Possible". Otherwise, print "Impossible".

**Jumping example:**

If a frog is at (4,0) and its jumping distance (k) is 2. Then during the next step the frog can be at one of the nine positions: (4,0), (4,2), (4,-2), (6,0), (6,2), (6,-2), (2,0), (2, 2), (2,-2).
Input

**Line 1:** Three space-separated integers `x1`, `y1` and `k1`.

**Line 2:** Three space-separated integers `x2`, `y2` and `k2`.

**Line 3:** Three space-separated integers `x3`, `y3` and `k3`.

Output

For each test case, print "Possible" if all 3 frogs can eventually meet, "Impossible" otherwise.

Constraints

-10000 ≤ `xi`,`yi` ≤ 10000

1 ≤ `ki` ≤ 100

All 3 frogs start at different locations.

Example

Input

7 0 1
2 -6 1
-1 0 2