diff --git a/day11/sample2 b/day11/sample2
new file mode 100644
index 0000000..d787665
--- /dev/null
+++ b/day11/sample2
@@ -0,0 +1,13 @@
+svr: aaa bbb
+aaa: fft
+fft: ccc
+bbb: tty
+tty: ccc
+ccc: ddd eee
+ddd: hub
+hub: fff
+eee: dac
+dac: fff
+fff: ggg hhh
+ggg: out
+hhh: out
diff --git a/day11/sol.py b/day11/sol.py
index eb444f9..cb48fbd 100644
--- a/day11/sol.py
+++ b/day11/sol.py
@@ -8,29 +8,66 @@ def solve(input):
         V.append(v)
         G[v] = parts
 
-    extra = [e for edges in G.values() for e in edges if e not in V]
-    V += extra
-    for v in extra:
+    sinks = [e for edges in G.values() for e in edges if e not in V]
+    V += sinks
+    for v in sinks:
         G[v] = []
 
+    # reversed graph
+    R = {}
+    for v, E in G.items():
+        for e in E:
+            R.setdefault(e, []).append(v)
 
-    Q = [(0,'you')]
-    dist = {}
-    paths = {v:0 for v in V}
-    paths['you'] = 1
-    while Q:
-        cost, v = heapq.heappop(Q)
-        if v in dist:
-            continue
-        dist[v] = cost
-        for e in G[v]:
-            if e not in dist:
-                heapq.heappush(Q, (cost+1, e))
-            paths[e] += paths[v]
-    print(paths)
-    print(paths['out'])
+    # topological sort
+    # T is an order of vertices such that each vertex is
+    # listed _after_ all the vertices connected to its incoming edges.
+    T = []
+    seen = set()
+    def visit(v):
+        if v not in seen:
+            seen.add(v)
+            for e in R.get(v,()):
+                visit(e)
+            T.append(v)
 
+    visit('out')
+    #T.reverse()
+    #print(T)
+
+    def paths(start,end):
+        Q = [(0,start)]
+        seen = set()
+        paths = {v:0 for v in V}
+        paths[start] = 1
+        for v in T:
+            if v in seen:
+                continue
+            seen.add(v)
+            for e in G[v]:
+                paths[e] += paths[v]
+        #print(paths)
+        return paths[end]
+
+    if 'you' in G:
+        # Part 1:
+        # find all paths from you -> out
+        print(paths('you', 'out'))
+
+    if 'svr' in G:
+        # Part 2: find all paths that pass through
+        # svr -> fft -> dac -> out, or
+        # svr -> dac -> fft -> out.
+        sf = paths('svr', 'fft')
+        sd = paths('svr', 'dac')
+        fd = paths('fft', 'dac')
+        df = paths('dac', 'fft')
+        do = paths('dac', 'out')
+        fo = paths('fft', 'out')
+
+        print(sf*fd*do + sd*df*fo)
 
 
 solve("sample")
+solve("sample2")
 solve("input")