import hashlib

def bin_sha256(x): return hashlib.sha256(x).digest()

def spread(L): return 16 if L == 9 else 3

def nodes(L): return 2**25 if L == 9 else 8**L

def to_binary(x): return '' if x == 0 else to_binary(int(x / 256)) + chr(x % 256)

def from_binary(x): return 0 if x == '' else 256 * from_binary(x[:-1]) + ord(x[-1])

def mine(root,difficulty,extranonce):
    layers = [[] for x in range(9)]
    layers[0] = [root]
    for L in range(1,10):
        prefix = root + to_binary(extranonce) + to_binary(L)
        for i in range(nodes(L)):
            p = []
            for k in range(spread(L)):
                h = bin_sha256(prefix + to_binary(i) + to_binary(k))
                ind = from_binary(h) % nodes(L-1)
                p.append(layers[L-1][ind])
            layers[L].append(bin_sha256(''.join(p)))
        print "Computed level ",L
    prefix = root + to_binary(extranonce)
    for i in range(2**26):
        p = []
        for k in range(4):
            h = bin_sha256(prefix + to_binary(i) + to_binary(k))
            ind = from_binary(h) % nodes(9)
            p.append(layers[9][ind])
        h = from_binary(bin_sha256(''.join(p)))
        if h * difficulty <= 2**256:
            return i
    return None

def verify(root,difficulty,extranonce,nonce):
    layers = [{} for x in range(9)]
    layers[0] = [root]
    def getnode(L,i):
        if i not in layers[L]:
            p = []
            for k in range(spread(L)):
                h = bin_sha256(root + to_binary(extranonce) + to_binary(L) + to_binary(o) + to_binary(k))
                ind = from_binary(h) % nodes(L-1)
                p.append(getnode(L-1,ind))
            layers[L][i] = bin_sha256(''.join(p))
        return layers[L][i]
    p = []
    for k in range(4):
        h = bin_sha256(root + to_binary(extranonce) + to_binary(nonce) + to_binary(k))
        ind = from_binary(h) % nodes(9)
        p.append(getnode(9,ind))
    h = from_binary(bin_sha256(''.join(p)))
    return h * difficulty <= 2**256