from copy import deepcopy
def find(x,cap,all_states):
    current=set()
    for i in range(3):
        for j in range(3):
            if i==j:
                continue
            new_state=deepcopy(list(x))
            temp=cap[i]-x[i]
            if temp<=x[j]:
                new_state[i]=cap[i]
                new_state[j]-=temp
            else:
                if new_state[i]+new_state[j]<=cap[i]:
                    new_state[i]=new_state[i]+new_state[j]
                    new_state[j]=0
            new_state=tuple(new_state)
            if new_state not in all_states:
                current.add(new_state)
    return current
def display(current,common,current_measures,index):
    print(str(index).center(10),end=":")
    t=""
    for i in current_measures:
        t+=str(i)
        t+=","
    print(t.center(25),end="")
    print(":",end="")
    for i in current:
        if i in common:
            print(i,"p2",end=" ")
        else:
            print(i,end=" ")
    print()
def make(given_state,index,cap,all_states,whole):
    common=set()
    current=set()
    current_measures=set()
    for each in given_state:
        t=find(each,cap,all_states)
        common=current.intersection(t)
        current=current.union(t)
    for each in current:
        for val in each:
            if val not in whole:
                current_measures.add(val)
    display(current,common,current_measures,index)
    whole=whole.union(current_measures)
    all_states=all_states.union(current)
    if current:
        make(current,index+1,cap,all_states,whole)

def prepare(x,cap):
    all_states=set()
    whole=set()
    for i in x:
        whole.add(i)
    all_states.add(x)
    print("step".center(10),end=" ")
    print("New Measurements".center(25),end=" ")
    print("New States".center(10))
    print("-"*80)
    print("0".center(10),end="")
    print(":",end="")
    initial=""
    for i in whole:
        initial+=str(i)
        initial+=","
    print(initial.center(25),end="")
    print(":",end="")
    print(x)
    make([x],1,cap,all_states,whole)
prepare((0,0,11),(3,5,11))
prepare((0,0,13),(3,5,13))
prepare((0,0,17),(3,5,17))
prepare((0,0,19),(3,5,19))
prepare((0,0,23),(3,5,23))