http://i.imgur.com/oulFbU2.png
k=rootnot permitted = 1not permitted = 46not permitted = 141not permitted = 78not permitted = 29not permitted = 31k=1k=29k=31k=32k=46k=47k=54k=57k=63k=70k=78k=79k=82k=86k=90k=98k=103k=104k=110k=111k=116k=120k=124k=128k=131k=141k=142k=143k=160r=2,109,110,116,118,119,155,30,76,77,32,33,103,47,57,63,70,82,86,98,104,131,95,48,49,154,50,51,52,53,54,62,67,92,127,139,120,58,59,60,61,68,69,64,65,66,125,124,126,81,157,158,159,160,161,71,72,73,74,75,138,128,79,80,90,91,129,130,83,84,85,93,87,88,89,96,97,156,99,100,101,102,6,108,105,106,107,111,112,113,114,137,115,117,121,172,173,174,175,164,165,166,167,168,169,170,171,132,133,134,135,136,142,143,144,145,146,147,148,149,150,151,152,153,162,163