working dict up to n=64

gistfile1.txt

0:
  (2, -1, -1) ('[]', '0')
1:
  (4, -1, -1) ('[[]]', '1')
2:
  (6, -1, -1) ('[[[]]]', '2')
3:
  (8, -1, -1) ('[[[[]]]]', '3')
4:
  (10, -1, -1) ('[[[[[]]]]]', '4')
  (13, 1, 1) ('[[[]]] [[[]]]', '2*2')
  (14, 2, 2) ('[[[]]]  [[[]]]', '2^2')
5:
  (12, -1, -1) ('[[[[[[]]]]]]', '5')
6:
  (14, -1, -1) ('[[[[[[[]]]]]]]', '6')
  (15, 1, 1) ('[[[[]]]] [[[]]]', '3*2')
7:
  (16, -1, -1) ('[[[[[[[[]]]]]]]]', '7')
8:
  (16, 2, 2) ('[[[]]]  [[[[]]]]', '2^3')
  (17, 1, 1) ('[[[[[]]]]] [[[]]]', '4*2')
  (18, -1, -1) ('[[[[[[[[[]]]]]]]]]', '8')
9:
  (16, 2, 2) ('[[[[]]]]  [[[]]]', '3^2')
  (17, 1, 1) ('[[[[]]]] [[[[]]]]', '3*3')
  (18, -1, -1) ('[[[[]]]  [[[[]]]]]', '(2^3+1)')
10:
  (18, -1, -1) ('[[[[[]]]]  [[[]]]]', '(3^2+1)')
  (19, 1, 1) ('[[[[[[]]]]]] [[[]]]', '5*2')
11:
  (21, -1, -1) ('[[[[[[[]]]]]] [[[]]]]', '(5*2+1)')
12:
  (19, 1, 1) ('[[[[[]]]]] [[[[]]]]', '4*3')
  (26, -1, -1) ('[[[[[[[[[[[[[]]]]]]]]]]]]]', '12')
13:
  (21, -1, -1) ('[[[[[[]]]]] [[[[]]]]]', '(4*3+1)')
14:
  (23, 1, 1) ('[[[[[[[[]]]]]]]] [[[]]]', '7*2')
  (30, -1, -1) ('[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]', '14')
15:
  (21, 1, 1) ('[[[[[[]]]]]] [[[[]]]]', '5*3')
  (25, -1, -1) ('[[[[[[[[[]]]]]]]] [[[]]]]', '(7*2+1)')
16:
  (17, 3, 3) ('[[[]]]   [[[[]]]]', '2^^3')
  (18, 2, 2) ('[[[[[]]]]]  [[[]]]', '4^2')
  (21, 1, 1) ('[[[[[]]]]] [[[[[]]]]]', '4*4')
  (23, -1, -1) ('[[[[[[[]]]]]] [[[[]]]]]', '(5*3+1)')
  (23, 1, 2) ('[[[]]]  [[[[]]]] [[[]]]', '2^3*2')
17:
  (20, -1, -1) ('[[[[[[]]]]]  [[[]]]]', '(4^2+1)')
18:
  (23, 1, 1) ('[[[[[[[]]]]]]] [[[[]]]]', '6*3')
  (23, 1, 2) ('[[[[]]]]  [[[]]] [[[]]]', '3^2*2')
19:
  (25, -1, -1) ('[[[[[[[[]]]]]]] [[[[]]]]]', '(6*3+1)')
20:
  (23, 1, 1) ('[[[[[[]]]]]] [[[[[]]]]]', '5*4')
21:
  (25, -1, -1) ('[[[[[[[]]]]]] [[[[[]]]]]]', '(5*4+1)')
  (25, 1, 1) ('[[[[[[[[]]]]]]]] [[[[]]]]', '7*3')
22:
  (27, -1, -1) ('[[[[[[[[[]]]]]]]] [[[[]]]]]', '(7*3+1)')
  (28, 1, 1) ('[[[[[[[]]]]]] [[[]]]] [[[]]]', '(5*2+1)*2')
23:
  (30, -1, -1) ('[[[[[[[[]]]]]] [[[]]]] [[[]]]]', '((5*2+1)*2+1)')
24:
  (25, 1, 1) ('[[[[[[[]]]]]]] [[[[[]]]]]', '6*4')
  (25, 1, 2) ('[[[]]]  [[[[]]]] [[[[]]]]', '2^3*3')
25:
  (20, 2, 2) ('[[[[[[]]]]]]  [[[]]]', '5^2')
  (25, 1, 1) ('[[[[[[]]]]]] [[[[[[]]]]]]', '5*5')
  (27, -1, -1) ('[[[[[[[[]]]]]]] [[[[[]]]]]]', '(6*4+1)')
26:
  (22, -1, -1) ('[[[[[[[]]]]]]  [[[]]]]', '(5^2+1)')
  (28, 1, 1) ('[[[[[[]]]]] [[[[]]]]] [[[]]]', '(4*3+1)*2')
27:
  (17, 3, 3) ('[[[[]]]]   [[[]]]', '3^^2')
  (18, 2, 2) ('[[[[]]]]  [[[[]]]]', '3^3')
  (25, 1, 2) ('[[[[]]]]  [[[]]] [[[[]]]]', '3^2*3')
  (30, -1, -1) ('[[[[[[[]]]]] [[[[]]]]] [[[]]]]', '((4*3+1)*2+1)')
28:
  (20, -1, -1) ('[[[[[]]]]  [[[[]]]]]', '(3^3+1)')
  (27, 1, 1) ('[[[[[[[[]]]]]]]] [[[[[]]]]]', '7*4')
29:
  (29, -1, -1) ('[[[[[[[[[]]]]]]]] [[[[[]]]]]]', '(7*4+1)')
30:
  (27, 1, 1) ('[[[[[[[]]]]]]] [[[[[[]]]]]]', '6*5')
31:
  (29, -1, -1) ('[[[[[[[[]]]]]]] [[[[[[]]]]]]]', '(6*5+1)')
32:
  (20, 2, 2) ('[[[]]]  [[[[[[]]]]]]', '2^5')
  (24, 1, 3) ('[[[]]]   [[[[]]]] [[[]]]', '2^^3*2')
  (27, 1, 2) ('[[[]]]  [[[[]]]] [[[[[]]]]]', '2^3*4')
33:
  (22, -1, -1) ('[[[[]]]  [[[[[[]]]]]]]', '(2^5+1)')
  (30, 1, 1) ('[[[[[[[]]]]]] [[[]]]] [[[[]]]]', '(5*2+1)*3')
34:
  (32, -1, -1) ('[[[[[[[[]]]]]] [[[]]]] [[[[]]]]]', '((5*2+1)*3+1)')
35:
  (29, 1, 1) ('[[[[[[[[]]]]]]]] [[[[[[]]]]]]', '7*5')
36:
  (22, 2, 2) ('[[[[[[[]]]]]]]  [[[]]]', '6^2')
  (27, 1, 2) ('[[[[]]]]  [[[]]] [[[[[]]]]]', '3^2*4')
  (28, 1, 1) ('[[[[[]]]]] [[[[]]]] [[[[]]]]', '4*3*3')
  (31, -1, -1) ('[[[[[[[[[]]]]]]]] [[[[[[]]]]]]]', '(7*5+1)')
37:
  (24, -1, -1) ('[[[[[[[[]]]]]]]  [[[]]]]', '(6^2+1)')
39:
  (30, 1, 1) ('[[[[[[]]]]] [[[[]]]]] [[[[]]]]', '(4*3+1)*3')
40:
  (29, 1, 1) ('[[[[[]]]]  [[[]]]] [[[[[]]]]]', '(3^2+1)*4')
  (29, 1, 2) ('[[[]]]  [[[[]]]] [[[[[[]]]]]]', '2^3*5')
  (32, -1, -1) ('[[[[[[[]]]]] [[[[]]]]] [[[[]]]]]', '((4*3+1)*3+1)')
41:
  (31, -1, -1) ('[[[[]]]  [[[[]]]] [[[[[[]]]]]]]', '(2^3*5+1)')
42:
  (31, 1, 1) ('[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]', '7*6')
43:
  (33, -1, -1) ('[[[[[[[[[]]]]]]]] [[[[[[[]]]]]]]]', '(7*6+1)')
44:
  (32, 1, 1) ('[[[[[[[]]]]]] [[[]]]] [[[[[]]]]]', '(5*2+1)*4')
45:
  (29, 1, 2) ('[[[[]]]]  [[[]]] [[[[[[]]]]]]', '3^2*5')
  (30, 1, 1) ('[[[[[[]]]]]] [[[[]]]] [[[[]]]]', '5*3*3')
  (34, -1, -1) ('[[[[[[[[]]]]]] [[[]]]] [[[[[]]]]]]', '((5*2+1)*4+1)')
46:
  (31, -1, -1) ('[[[[[]]]]  [[[]]] [[[[[[]]]]]]]', '(3^2*5+1)')
48:
  (26, 1, 3) ('[[[]]]   [[[[]]]] [[[[]]]]', '2^^3*3')
  (30, 1, 1) ('[[[[[]]]]] [[[[]]]] [[[[[]]]]]', '4*3*4')
  (31, 1, 2) ('[[[]]]  [[[[]]]] [[[[[[[]]]]]]]', '2^3*6')
49:
  (24, 2, 2) ('[[[[[[[[]]]]]]]]  [[[]]]', '7^2')
  (28, -1, -1) ('[[[[]]]   [[[[]]]] [[[[]]]]]', '(2^^3*3+1)')
  (33, 1, 1) ('[[[[[[[[]]]]]]]] [[[[[[[[]]]]]]]]', '7*7')
50:
  (26, -1, -1) ('[[[[[[[[[]]]]]]]]  [[[]]]]', '(7^2+1)')
  (31, 1, 1) ('[[[[[]]]]  [[[]]]] [[[[[[]]]]]]', '(3^2+1)*5')
51:
  (33, -1, -1) ('[[[[[[]]]]  [[[]]]] [[[[[[]]]]]]]', '((3^2+1)*5+1)')
52:
  (32, 1, 1) ('[[[[[[]]]]] [[[[]]]]] [[[[[]]]]]', '(4*3+1)*4')
53:
  (34, -1, -1) ('[[[[[[[]]]]] [[[[]]]]] [[[[[]]]]]]', '((4*3+1)*4+1)')
54:
  (31, 1, 2) ('[[[[]]]]  [[[]]] [[[[[[[]]]]]]]', '3^2*6')
55:
  (33, -1, -1) ('[[[[[]]]]  [[[]]] [[[[[[[]]]]]]]]', '(3^2*6+1)')
  (34, 1, 1) ('[[[[[[[]]]]]] [[[]]]] [[[[[[]]]]]]', '(5*2+1)*5')
56:
  (33, 1, 2) ('[[[]]]  [[[[]]]] [[[[[[[[]]]]]]]]', '2^3*7')
  (34, 1, 1) ('[[[[[[[[]]]]]]]] [[[]]] [[[[[]]]]]', '7*2*4')
  (36, -1, -1) ('[[[[[[[[]]]]]] [[[]]]] [[[[[[]]]]]]]', '((5*2+1)*5+1)')
57:
  (35, -1, -1) ('[[[[]]]  [[[[]]]] [[[[[[[[]]]]]]]]]', '(2^3*7+1)')
60:
  (32, 1, 1) ('[[[[[]]]]] [[[[]]]] [[[[[[]]]]]]', '4*3*5')
61:
  (34, -1, -1) ('[[[[[[]]]]] [[[[]]]] [[[[[[]]]]]]]', '(4*3*5+1)')
63:
  (33, 1, 2) ('[[[[]]]]  [[[]]] [[[[[[[[]]]]]]]]', '3^2*7')
64:
  (20, 2, 2) ('[[[[[]]]]]  [[[[]]]]', '4^3')
  (28, 1, 3) ('[[[]]]   [[[[]]]] [[[[[]]]]]', '2^^3*4')
  (33, 1, 2) ('[[[]]]  [[[[]]]] [[[]]]  [[[[]]]]', '2^3*2^3')
  (35, -1, -1) ('[[[[[]]]]  [[[]]] [[[[[[[[]]]]]]]]]', '(3^2*7+1)')
65:
  (22, -1, -1) ('[[[[[[]]]]]  [[[[]]]]]', '(4^3+1)')
  (34, 1, 1) ('[[[[[[]]]]] [[[[]]]]] [[[[[[]]]]]]', '(4*3+1)*5')
66:
  (36, -1, -1) ('[[[[[[[]]]]] [[[[]]]]] [[[[[[]]]]]]]', '((4*3+1)*5+1)')
  (36, 1, 1) ('[[[[[[[]]]]]] [[[]]]] [[[[[[[]]]]]]]', '(5*2+1)*6')
67:
  (38, -1, -1) ('[[[[[[[[]]]]]] [[[]]]] [[[[[[[]]]]]]]]', '((5*2+1)*6+1)')
70:
  (35, 1, 1) ('[[[[[]]]]  [[[]]]] [[[[[[[[]]]]]]]]', '(3^2+1)*7')
71:
  (37, -1, -1) ('[[[[[[]]]]  [[[]]]] [[[[[[[[]]]]]]]]]', '((3^2+1)*7+1)')
72:
  (33, 1, 2) ('[[[[]]]]  [[[]]] [[[]]]  [[[[]]]]', '3^2*2^3')
  (34, 1, 1) ('[[[[[]]]]] [[[[]]]] [[[[[[[]]]]]]]', '4*3*6')
73:
  (35, -1, -1) ('[[[[[]]]]  [[[]]] [[[]]]  [[[[]]]]]', '(3^2*2^3+1)')
75:
  (34, 1, 1) ('[[[[[[]]]]]] [[[[]]]] [[[[[[]]]]]]', '5*3*5')
76:
  (36, -1, -1) ('[[[[[[[]]]]]] [[[[]]]] [[[[[[]]]]]]]', '(5*3*5+1)')
77:
  (38, 1, 1) ('[[[[[[[]]]]]] [[[]]]] [[[[[[[[]]]]]]]]', '(5*2+1)*7')
78:
  (36, 1, 1) ('[[[[[[]]]]] [[[[]]]]] [[[[[[[]]]]]]]', '(4*3+1)*6')
  (40, -1, -1) ('[[[[[[[[]]]]]] [[[]]]] [[[[[[[[]]]]]]]]]', '((5*2+1)*7+1)')
79:
  (38, -1, -1) ('[[[[[[[]]]]] [[[[]]]]] [[[[[[[]]]]]]]]', '((4*3+1)*6+1)')
80:
  (30, 1, 3) ('[[[]]]   [[[[]]]] [[[[[[]]]]]]', '2^^3*5')
  (35, 1, 2) ('[[[[[]]]]  [[[]]]] [[[]]]  [[[[]]]]', '(3^2+1)*2^3')
81:
  (20, 2, 2) ('[[[[]]]]  [[[[[]]]]]', '3^4')
  (32, -1, -1) ('[[[[]]]   [[[[]]]] [[[[[[]]]]]]]', '(2^^3*5+1)')
  (33, 1, 2) ('[[[[]]]]  [[[]]] [[[[]]]]  [[[]]]', '3^2*3^2')
82:
  (22, -1, -1) ('[[[[[]]]]  [[[[[]]]]]]', '(3^4+1)')
84:
  (36, 1, 1) ('[[[[[]]]]] [[[[]]]] [[[[[[[[]]]]]]]]', '4*3*7')
85:
  (38, -1, -1) ('[[[[[[]]]]] [[[[]]]] [[[[[[[[]]]]]]]]]', '(4*3*7+1)')
88:
  (38, 1, 2) ('[[[[[[[]]]]]] [[[]]]] [[[]]]  [[[[]]]]', '(5*2+1)*2^3')
89:
  (40, -1, -1) ('[[[[[[[[]]]]]] [[[]]]] [[[]]]  [[[[]]]]]', '((5*2+1)*2^3+1)')
90:
  (35, 1, 2) ('[[[[[]]]]  [[[]]]] [[[[]]]]  [[[]]]', '(3^2+1)*3^2')
  (36, 1, 1) ('[[[[[[]]]]]] [[[[]]]] [[[[[[[]]]]]]]', '5*3*6')
91:
  (37, -1, -1) ('[[[[[[]]]]  [[[]]]] [[[[]]]]  [[[]]]]', '((3^2+1)*3^2+1)')
  (38, 1, 1) ('[[[[[[]]]]] [[[[]]]]] [[[[[[[[]]]]]]]]', '(4*3+1)*7')
92:
  (40, -1, -1) ('[[[[[[[]]]]] [[[[]]]]] [[[[[[[[]]]]]]]]]', '((4*3+1)*7+1)')
96:
  (32, 1, 3) ('[[[]]]   [[[[]]]] [[[[[[[]]]]]]]', '2^^3*6')
  (36, 1, 2) ('[[[[[]]]]] [[[[]]]] [[[]]]  [[[[]]]]', '4*3*2^3')
97:
  (34, -1, -1) ('[[[[]]]   [[[[]]]] [[[[[[[]]]]]]]]', '(2^^3*6+1)')
98:
  (40, 1, 1) ('[[[[[[[[]]]]]]]] [[[]]] [[[[[[[[]]]]]]]]', '7*2*7')
99:
  (38, 1, 2) ('[[[[[[[]]]]]] [[[]]]] [[[[]]]]  [[[]]]', '(5*2+1)*3^2')
  (42, -1, -1) ('[[[[[[[[[]]]]]]]] [[[]]] [[[[[[[[]]]]]]]]]', '(7*2*7+1)')
100:
  (26, 2, 2) ('[[[[[]]]]  [[[]]]]  [[[]]]', '(3^2+1)^2')
  (37, 1, 1) ('[[[[[]]]]  [[[]]]] [[[[[]]]]  [[[]]]]', '(3^2+1)*(3^2+1)')
  (40, -1, -1) ('[[[[[[[[]]]]]] [[[]]]] [[[[]]]]  [[[]]]]', '((5*2+1)*3^2+1)')
101:
  (28, -1, -1) ('[[[[[[]]]]  [[[]]]]  [[[]]]]', '((3^2+1)^2+1)')
104:
  (38, 1, 2) ('[[[[[[]]]]] [[[[]]]]] [[[]]]  [[[[]]]]', '(4*3+1)*2^3')
105:
  (38, 1, 1) ('[[[[[[]]]]]] [[[[]]]] [[[[[[[[]]]]]]]]', '5*3*7')
  (40, -1, -1) ('[[[[[[[]]]]] [[[[]]]]] [[[]]]  [[[[]]]]]', '((4*3+1)*2^3+1)')
106:
  (40, -1, -1) ('[[[[[[[]]]]]] [[[[]]]] [[[[[[[[]]]]]]]]]', '(5*3*7+1)')
108:
  (36, 1, 2) ('[[[[[]]]]] [[[[]]]] [[[[]]]]  [[[]]]', '4*3*3^2')
109:
  (38, -1, -1) ('[[[[[[]]]]] [[[[]]]] [[[[]]]]  [[[]]]]', '(4*3*3^2+1)')
110:
  (40, 1, 1) ('[[[[[[[]]]]]] [[[]]]] [[[[[]]]]  [[[]]]]', '(5*2+1)*(3^2+1)')
111:
  (42, -1, -1) ('[[[[[[[[]]]]]] [[[]]]] [[[[[]]]]  [[[]]]]]', '((5*2+1)*(3^2+1)+1)')
112:
  (34, 1, 3) ('[[[]]]   [[[[]]]] [[[[[[[[]]]]]]]]', '2^^3*7')
  (40, 1, 2) ('[[[[[[[[]]]]]]]] [[[]]] [[[]]]  [[[[]]]]', '7*2*2^3')
113:
  (36, -1, -1) ('[[[[]]]   [[[[]]]] [[[[[[[[]]]]]]]]]', '(2^^3*7+1)')
117:
  (38, 1, 2) ('[[[[[[]]]]] [[[[]]]]] [[[[]]]]  [[[]]]', '(4*3+1)*3^2')
118:
  (40, -1, -1) ('[[[[[[[]]]]] [[[[]]]]] [[[[]]]]  [[[]]]]', '((4*3+1)*3^2+1)')
120:
  (38, 1, 1) ('[[[[[]]]]] [[[[]]]] [[[[[]]]]  [[[]]]]', '4*3*(3^2+1)')
  (38, 1, 2) ('[[[[[[]]]]]] [[[[]]]] [[[]]]  [[[[]]]]', '5*3*2^3')
121:
  (29, 2, 2) ('[[[[[[[]]]]]] [[[]]]]  [[[]]]', '(5*2+1)^2')
  (40, -1, -1) ('[[[[[[]]]]] [[[[]]]] [[[[[]]]]  [[[]]]]]', '(4*3*(3^2+1)+1)')
  (43, 1, 1) ('[[[[[[[]]]]]] [[[]]]] [[[[[[[]]]]]] [[[]]]]', '(5*2+1)*(5*2+1)')
122:
  (31, -1, -1) ('[[[[[[[[]]]]]] [[[]]]]  [[[]]]]', '((5*2+1)^2+1)')
125:
  (22, 2, 2) ('[[[[[[]]]]]]  [[[[]]]]', '5^3')
126:
  (24, -1, -1) ('[[[[[[[]]]]]]  [[[[]]]]]', '(5^3+1)')
  (40, 1, 2) ('[[[[[[[[]]]]]]]] [[[]]] [[[[]]]]  [[[]]]', '7*2*3^2')
127:
  (42, -1, -1) ('[[[[[[[[[]]]]]]]] [[[]]] [[[[]]]]  [[[]]]]', '(7*2*3^2+1)')
128:
  (24, 2, 2) ('[[[]]]  [[[[[[[[]]]]]]]]', '2^7')
  (34, 1, 3) ('[[[]]]   [[[[]]]] [[[]]]  [[[[]]]]', '2^^3*2^3')
129:
  (26, -1, -1) ('[[[[]]]  [[[[[[[[]]]]]]]]]', '(2^7+1)')
130:
  (40, 1, 1) ('[[[[[[]]]]] [[[[]]]]] [[[[[]]]]  [[[]]]]', '(4*3+1)*(3^2+1)')
131:
  (42, -1, -1) ('[[[[[[[]]]]] [[[[]]]]] [[[[[]]]]  [[[]]]]]', '((4*3+1)*(3^2+1)+1)')
132:
  (41, 1, 1) ('[[[[[]]]]] [[[[]]]] [[[[[[[]]]]]] [[[]]]]', '4*3*(5*2+1)')
133:
  (43, -1, -1) ('[[[[[[]]]]] [[[[]]]] [[[[[[[]]]]]] [[[]]]]]', '(4*3*(5*2+1)+1)')
135:
  (38, 1, 2) ('[[[[[[]]]]]] [[[[]]]] [[[[]]]]  [[[]]]', '5*3*3^2')
136:
  (40, -1, -1) ('[[[[[[[]]]]]] [[[[]]]] [[[[]]]]  [[[]]]]', '(5*3*3^2+1)')
140:
  (42, 1, 1) ('[[[[[[[[]]]]]]]] [[[]]] [[[[[]]]]  [[[]]]]', '7*2*(3^2+1)')
141:
  (44, -1, -1) ('[[[[[[[[[]]]]]]]] [[[]]] [[[[[]]]]  [[[]]]]]', '(7*2*(3^2+1)+1)')
143:
  (43, 1, 1) ('[[[[[[]]]]] [[[[]]]]] [[[[[[[]]]]]] [[[]]]]', '(4*3+1)*(5*2+1)')
144:
  (34, 1, 3) ('[[[]]]   [[[[]]]] [[[[]]]]  [[[]]]', '2^^3*3^2')
  (34, 2, 2) ('[[[[[[[[[[[[[]]]]]]]]]]]]]  [[[]]]', '12^2')
  (39, 1, 1) ('[[[[[]]]]] [[[[]]]] [[[[[]]]]] [[[[]]]]', '4*3*4*3')
  (45, -1, -1) ('[[[[[[[]]]]] [[[[]]]]] [[[[[[[]]]]]] [[[]]]]]', '((4*3+1)*(5*2+1)+1)')
145:
  (36, -1, -1) ('[[[[[[[[[[[[[[]]]]]]]]]]]]]  [[[]]]]', '(12^2+1)')
150:
  (40, 1, 1) ('[[[[[[]]]]]] [[[[]]]] [[[[[]]]]  [[[]]]]', '5*3*(3^2+1)')
151:
  (42, -1, -1) ('[[[[[[[]]]]]] [[[[]]]] [[[[[]]]]  [[[]]]]]', '(5*3*(3^2+1)+1)')
154:
  (45, 1, 1) ('[[[[[[[[]]]]]]]] [[[]]] [[[[[[[]]]]]] [[[]]]]', '7*2*(5*2+1)')
155:
  (47, -1, -1) ('[[[[[[[[[]]]]]]]] [[[]]] [[[[[[[]]]]]] [[[]]]]]', '(7*2*(5*2+1)+1)')
156:
  (41, 1, 1) ('[[[[[[]]]]] [[[[]]]]] [[[[[]]]]] [[[[]]]]', '(4*3+1)*4*3')
157:
  (43, -1, -1) ('[[[[[[[]]]]] [[[[]]]]] [[[[[]]]]] [[[[]]]]]', '((4*3+1)*4*3+1)')
160:
  (36, 1, 3) ('[[[]]]   [[[[]]]] [[[[[]]]]  [[[]]]]', '2^^3*(3^2+1)')
161:
  (38, -1, -1) ('[[[[]]]   [[[[]]]] [[[[[]]]]  [[[]]]]]', '(2^^3*(3^2+1)+1)')
165:
  (43, 1, 1) ('[[[[[[]]]]]] [[[[]]]] [[[[[[[]]]]]] [[[]]]]', '5*3*(5*2+1)')
166:
  (45, -1, -1) ('[[[[[[[]]]]]] [[[[]]]] [[[[[[[]]]]]] [[[]]]]]', '(5*3*(5*2+1)+1)')
168:
  (43, 1, 1) ('[[[[[[[[]]]]]]]] [[[]]] [[[[[]]]]] [[[[]]]]', '7*2*4*3')
169:
  (29, 2, 2) ('[[[[[[]]]]] [[[[]]]]]  [[[]]]', '(4*3+1)^2')
  (43, 1, 1) ('[[[[[[]]]]] [[[[]]]]] [[[[[[]]]]] [[[[]]]]]', '(4*3+1)*(4*3+1)')
  (45, -1, -1) ('[[[[[[[[[]]]]]]]] [[[]]] [[[[[]]]]] [[[[]]]]]', '(7*2*4*3+1)')
170:
  (31, -1, -1) ('[[[[[[[]]]]] [[[[]]]]]  [[[]]]]', '((4*3+1)^2+1)')
176:
  (39, 1, 3) ('[[[]]]   [[[[]]]] [[[[[[[]]]]]] [[[]]]]', '2^^3*(5*2+1)')
177:
  (41, -1, -1) ('[[[[]]]   [[[[]]]] [[[[[[[]]]]]] [[[]]]]]', '(2^^3*(5*2+1)+1)')
180:
  (41, 1, 1) ('[[[[[[]]]]]] [[[[]]]] [[[[[]]]]] [[[[]]]]', '5*3*4*3')
181:
  (43, -1, -1) ('[[[[[[[]]]]]] [[[[]]]] [[[[[]]]]] [[[[]]]]]', '(5*3*4*3+1)')
182:
  (45, 1, 1) ('[[[[[[[[]]]]]]]] [[[]]] [[[[[[]]]]] [[[[]]]]]', '7*2*(4*3+1)')
183:
  (47, -1, -1) ('[[[[[[[[[]]]]]]]] [[[]]] [[[[[[]]]]] [[[[]]]]]]', '(7*2*(4*3+1)+1)')
192:
  (37, 1, 3) ('[[[]]]   [[[[]]]] [[[[[]]]]] [[[[]]]]', '2^^3*4*3')
193:
  (39, -1, -1) ('[[[[]]]   [[[[]]]] [[[[[]]]]] [[[[]]]]]', '(2^^3*4*3+1)')
195:
  (43, 1, 1) ('[[[[[[]]]]]] [[[[]]]] [[[[[[]]]]] [[[[]]]]]', '5*3*(4*3+1)')
196:
  (38, 2, 2) ('[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]  [[[]]]', '14^2')
  (45, -1, -1) ('[[[[[[[]]]]]] [[[[]]]] [[[[[[]]]]] [[[[]]]]]]', '(5*3*(4*3+1)+1)')
  (47, 1, 1) ('[[[[[[[[]]]]]]]] [[[]]] [[[[[[[[]]]]]]]] [[[]]]', '7*2*7*2')
197:
  (40, -1, -1) ('[[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]  [[[]]]]', '(14^2+1)')
208:
  (39, 1, 3) ('[[[]]]   [[[[]]]] [[[[[[]]]]] [[[[]]]]]', '2^^3*(4*3+1)')
209:
  (41, -1, -1) ('[[[[]]]   [[[[]]]] [[[[[[]]]]] [[[[]]]]]]', '(2^^3*(4*3+1)+1)')
210:
  (45, 1, 1) ('[[[[[[]]]]]] [[[[]]]] [[[[[[[[]]]]]]]] [[[]]]', '5*3*7*2')
211:
  (47, -1, -1) ('[[[[[[[]]]]]] [[[[]]]] [[[[[[[[]]]]]]]] [[[]]]]', '(5*3*7*2+1)')
216:
  (24, 2, 2) ('[[[[[[[]]]]]]]  [[[[]]]]', '6^3')
217:
  (26, -1, -1) ('[[[[[[[[]]]]]]]  [[[[]]]]]', '(6^3+1)')
224:
  (41, 1, 3) ('[[[]]]   [[[[]]]] [[[[[[[[]]]]]]]] [[[]]]', '2^^3*7*2')
225:
  (33, 2, 2) ('[[[[[[[[[]]]]]]]] [[[]]]]  [[[]]]', '(7*2+1)^2')
  (43, -1, -1) ('[[[[]]]   [[[[]]]] [[[[[[[[]]]]]]]] [[[]]]]', '(2^^3*7*2+1)')
  (43, 1, 1) ('[[[[[[]]]]]] [[[[]]]] [[[[[[]]]]]] [[[[]]]]', '5*3*5*3')
226:
  (35, -1, -1) ('[[[[[[[[[[]]]]]]]] [[[]]]]  [[[]]]]', '((7*2+1)^2+1)')
240:
  (39, 1, 3) ('[[[]]]   [[[[]]]] [[[[[[]]]]]] [[[[]]]]', '2^^3*5*3')
241:
  (41, -1, -1) ('[[[[]]]   [[[[]]]] [[[[[[]]]]]] [[[[]]]]]', '(2^^3*5*3+1)')
243:
  (22, 2, 2) ('[[[[]]]]  [[[[[[]]]]]]', '3^5')
244:
  (24, -1, -1) ('[[[[[]]]]  [[[[[[]]]]]]]', '(3^5+1)')
256:
  (19, 3, 3) ('[[[[[]]]]]   [[[]]]', '4^^2')
  (22, 2, 2) ('[[[[[]]]]]  [[[[[]]]]]', '4^4')
  (25, 2, 3) ('[[[]]]   [[[[]]]]  [[[]]]', '2^^3^2')
  (35, 1, 3) ('[[[]]]   [[[[]]]] [[[]]]   [[[[]]]]', '2^^3*2^^3')
257:
  (24, -1, -1) ('[[[[[[]]]]]  [[[[[]]]]]]', '(4^4+1)')
343:
  (26, 2, 2) ('[[[[[[[[]]]]]]]]  [[[[]]]]', '7^3')
344:
  (28, -1, -1) ('[[[[[[[[[]]]]]]]]  [[[[]]]]]', '(7^3+1)')
512:
  (26, 2, 2) ('[[[]]]  [[[[]]]  [[[[]]]]]', '2^(2^3+1)')
513:
  (28, -1, -1) ('[[[[]]]  [[[[]]]  [[[[]]]]]]', '(2^(2^3+1)+1)')
625:
  (24, 2, 2) ('[[[[[[]]]]]]  [[[[[]]]]]', '5^4')
626:
  (26, -1, -1) ('[[[[[[[]]]]]]  [[[[[]]]]]]', '(5^4+1)')
729:
  (24, 2, 2) ('[[[[]]]]  [[[[[[[]]]]]]]', '3^6')
730:
  (26, -1, -1) ('[[[[[]]]]  [[[[[[[]]]]]]]]', '(3^6+1)')
1000:
  (28, 2, 2) ('[[[[[]]]]  [[[]]]]  [[[[]]]]', '(3^2+1)^3')
1001:
  (30, -1, -1) ('[[[[[[]]]]  [[[]]]]  [[[[]]]]]', '((3^2+1)^3+1)')
1024:
  (24, 2, 2) ('[[[[[]]]]]  [[[[[[]]]]]]', '4^5')
1025:
  (26, -1, -1) ('[[[[[[]]]]]  [[[[[[]]]]]]]', '(4^5+1)')
1296:
  (26, 2, 2) ('[[[[[[[]]]]]]]  [[[[[]]]]]', '6^4')
1297:
  (28, -1, -1) ('[[[[[[[[]]]]]]]  [[[[[]]]]]]', '(6^4+1)')
1331:
  (31, 2, 2) ('[[[[[[[]]]]]] [[[]]]]  [[[[]]]]', '(5*2+1)^3')
1332:
  (33, -1, -1) ('[[[[[[[[]]]]]] [[[]]]]  [[[[]]]]]', '((5*2+1)^3+1)')
1728:
  (36, 2, 2) ('[[[[[[[[[[[[[]]]]]]]]]]]]]  [[[[]]]]', '12^3')
1729:
  (38, -1, -1) ('[[[[[[[[[[[[[[]]]]]]]]]]]]]  [[[[]]]]]', '(12^3+1)')
2048:
  (29, 2, 2) ('[[[]]]  [[[[[[[]]]]]] [[[]]]]', '2^(5*2+1)')
2049:
  (31, -1, -1) ('[[[[]]]  [[[[[[[]]]]]] [[[]]]]]', '(2^(5*2+1)+1)')
2187:
  (26, 2, 2) ('[[[[]]]]  [[[[[[[[]]]]]]]]', '3^7')
2188:
  (28, -1, -1) ('[[[[[]]]]  [[[[[[[[]]]]]]]]]', '(3^7+1)')
2197:
  (31, 2, 2) ('[[[[[[]]]]] [[[[]]]]]  [[[[]]]]', '(4*3+1)^3')
2198:
  (33, -1, -1) ('[[[[[[[]]]]] [[[[]]]]]  [[[[]]]]]', '((4*3+1)^3+1)')
2401:
  (28, 2, 2) ('[[[[[[[[]]]]]]]]  [[[[[]]]]]', '7^4')
2402:
  (30, -1, -1) ('[[[[[[[[[]]]]]]]]  [[[[[]]]]]]', '(7^4+1)')
2744:
  (40, 2, 2) ('[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]  [[[[]]]]', '14^3')
2745:
  (42, -1, -1) ('[[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]  [[[[]]]]]', '(14^3+1)')
3125:
  (21, 3, 3) ('[[[[[[]]]]]]   [[[]]]', '5^^2')
  (26, 2, 2) ('[[[[[[]]]]]]  [[[[[[]]]]]]', '5^5')
3126:
  (28, -1, -1) ('[[[[[[[]]]]]]  [[[[[[]]]]]]]', '(5^5+1)')
3375:
  (35, 2, 2) ('[[[[[[[[[]]]]]]]] [[[]]]]  [[[[]]]]', '(7*2+1)^3')
3376:
  (37, -1, -1) ('[[[[[[[[[[]]]]]]]] [[[]]]]  [[[[]]]]]', '((7*2+1)^3+1)')
4096:
  (26, 2, 2) ('[[[[[]]]]]  [[[[[[[]]]]]]]', '4^6')
  (27, 2, 3) ('[[[]]]   [[[[]]]]  [[[[]]]]', '2^^3^3')
4097:
  (28, -1, -1) ('[[[[[[]]]]]  [[[[[[[]]]]]]]]', '(4^6+1)')
6561:
  (28, 2, 2) ('[[[[]]]]  [[[[[[[[[]]]]]]]]]', '3^8')
6562:
  (30, -1, -1) ('[[[[[]]]]  [[[[[[[[[]]]]]]]]]]', '(3^8+1)')
7776:
  (28, 2, 2) ('[[[[[[[]]]]]]]  [[[[[[]]]]]]', '6^5')
7777:
  (30, -1, -1) ('[[[[[[[[]]]]]]]  [[[[[[]]]]]]]', '(6^5+1)')
8192:
  (29, 2, 2) ('[[[]]]  [[[[[[]]]]] [[[[]]]]]', '2^(4*3+1)')
8193:
  (31, -1, -1) ('[[[[]]]  [[[[[[]]]]] [[[[]]]]]]', '(2^(4*3+1)+1)')
10000:
  (30, 2, 2) ('[[[[[]]]]  [[[]]]]  [[[[[]]]]]', '(3^2+1)^4')
10001:
  (32, -1, -1) ('[[[[[[]]]]  [[[]]]]  [[[[[]]]]]]', '((3^2+1)^4+1)')
14641:
  (33, 2, 2) ('[[[[[[[]]]]]] [[[]]]]  [[[[[]]]]]', '(5*2+1)^4')
14642:
  (35, -1, -1) ('[[[[[[[[]]]]]] [[[]]]]  [[[[[]]]]]]', '((5*2+1)^4+1)')
15625:
  (28, 2, 2) ('[[[[[[]]]]]]  [[[[[[[]]]]]]]', '5^6')
15626:
  (30, -1, -1) ('[[[[[[[]]]]]]  [[[[[[[]]]]]]]]', '(5^6+1)')
16384:
  (28, 2, 2) ('[[[[[]]]]]  [[[[[[[[]]]]]]]]', '4^7')
16385:
  (30, -1, -1) ('[[[[[[]]]]]  [[[[[[[[]]]]]]]]]', '(4^7+1)')
16807:
  (30, 2, 2) ('[[[[[[[[]]]]]]]]  [[[[[[]]]]]]', '7^5')
16808:
  (32, -1, -1) ('[[[[[[[[[]]]]]]]]  [[[[[[]]]]]]]', '(7^5+1)')
19683:
  (28, 2, 2) ('[[[[]]]]  [[[[]]]  [[[[]]]]]', '3^(2^3+1)')
19684:
  (30, -1, -1) ('[[[[[]]]]  [[[[]]]  [[[[]]]]]]', '(3^(2^3+1)+1)')
20736:
  (38, 2, 2) ('[[[[[[[[[[[[[]]]]]]]]]]]]]  [[[[[]]]]]', '12^4')
20737:
  (40, -1, -1) ('[[[[[[[[[[[[[[]]]]]]]]]]]]]  [[[[[]]]]]]', '(12^4+1)')
28561:
  (33, 2, 2) ('[[[[[[]]]]] [[[[]]]]]  [[[[[]]]]]', '(4*3+1)^4')
28562:
  (35, -1, -1) ('[[[[[[[]]]]] [[[[]]]]]  [[[[[]]]]]]', '((4*3+1)^4+1)')
32768:
  (32, 2, 2) ('[[[[[[[[[]]]]]]]]]  [[[[[[]]]]]]', '8^5')
32769:
  (34, -1, -1) ('[[[[[[[[[[]]]]]]]]]  [[[[[[]]]]]]]', '(8^5+1)')
38416:
  (42, 2, 2) ('[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]  [[[[[]]]]]', '14^4')
38417:
  (44, -1, -1) ('[[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]  [[[[[]]]]]]', '(14^4+1)')
46656:
  (23, 3, 3) ('[[[[[[[]]]]]]]   [[[]]]', '6^^2')
  (30, 2, 2) ('[[[[[[[]]]]]]]  [[[[[[[]]]]]]]', '6^6')
46657:
  (32, -1, -1) ('[[[[[[[[]]]]]]]  [[[[[[[]]]]]]]]', '(6^6+1)')
50625:
  (37, 2, 2) ('[[[[[[[[[]]]]]]]] [[[]]]]  [[[[[]]]]]', '(7*2+1)^4')
50626:
  (39, -1, -1) ('[[[[[[[[[[]]]]]]]] [[[]]]]  [[[[[]]]]]]', '((7*2+1)^4+1)')
59049:
  (28, 2, 2) ('[[[[]]]]  [[[[[]]]]  [[[]]]]', '3^(3^2+1)')
59050:
  (30, -1, -1) ('[[[[[]]]]  [[[[[]]]]  [[[]]]]]', '(3^(3^2+1)+1)')
65536:
  (18, 4, 4) ('[[[]]]    [[[[]]]]', '2^^^3')
  (25, 2, 3) ('[[[]]]  [[[]]]   [[[[]]]]', '2^2^^3')
  (30, 2, 2) ('[[[[[]]]]]  [[[[[[[[[]]]]]]]]]', '4^8')
65537:
  (27, -1, -1) ('[[[[]]]  [[[]]]   [[[[]]]]]', '(2^2^^3+1)')
78125:
  (30, 2, 2) ('[[[[[[]]]]]]  [[[[[[[[]]]]]]]]', '5^7')
78126:
  (32, -1, -1) ('[[[[[[[]]]]]]  [[[[[[[[]]]]]]]]]', '(5^7+1)')
100000:
  (32, 2, 2) ('[[[[[]]]]  [[[]]]]  [[[[[[]]]]]]', '(3^2+1)^5')
100001:
  (34, -1, -1) ('[[[[[[]]]]  [[[]]]]  [[[[[[]]]]]]]', '((3^2+1)^5+1)')
117649:
  (32, 2, 2) ('[[[[[[[[]]]]]]]]  [[[[[[[]]]]]]]', '7^6')
117650:
  (34, -1, -1) ('[[[[[[[[[]]]]]]]]  [[[[[[[]]]]]]]]', '(7^6+1)')
161051:
  (35, 2, 2) ('[[[[[[[]]]]]] [[[]]]]  [[[[[[]]]]]]', '(5*2+1)^5')
161052:
  (37, -1, -1) ('[[[[[[[[]]]]]] [[[]]]]  [[[[[[]]]]]]]', '((5*2+1)^5+1)')
177147:
  (31, 2, 2) ('[[[[]]]]  [[[[[[[]]]]]] [[[]]]]', '3^(5*2+1)')
177148:
  (33, -1, -1) ('[[[[[]]]]  [[[[[[[]]]]]] [[[]]]]]', '(3^(5*2+1)+1)')
248832:
  (40, 2, 2) ('[[[[[[[[[[[[[]]]]]]]]]]]]]  [[[[[[]]]]]]', '12^5')
248833:
  (42, -1, -1) ('[[[[[[[[[[[[[[]]]]]]]]]]]]]  [[[[[[]]]]]]]', '(12^5+1)')
262144:
  (30, 2, 2) ('[[[[[]]]]]  [[[[]]]  [[[[]]]]]', '4^(2^3+1)')
262145:
  (32, -1, -1) ('[[[[[[]]]]]  [[[[]]]  [[[[]]]]]]', '(4^(2^3+1)+1)')
279936:
  (32, 2, 2) ('[[[[[[[]]]]]]]  [[[[[[[[]]]]]]]]', '6^7')
279937:
  (34, -1, -1) ('[[[[[[[[]]]]]]]  [[[[[[[[]]]]]]]]]', '(6^7+1)')
371293:
  (35, 2, 2) ('[[[[[[]]]]] [[[[]]]]]  [[[[[[]]]]]]', '(4*3+1)^5')
371294:
  (37, -1, -1) ('[[[[[[[]]]]] [[[[]]]]]  [[[[[[]]]]]]]', '((4*3+1)^5+1)')
390625:
  (32, 2, 2) ('[[[[[[]]]]]]  [[[[[[[[[]]]]]]]]]', '5^8')
390626:
  (34, -1, -1) ('[[[[[[[]]]]]]  [[[[[[[[[]]]]]]]]]]', '(5^8+1)')
531441:
  (34, 2, 2) ('[[[[]]]  [[[[]]]]]  [[[[[[[]]]]]]]', '(2^3+1)^6')
531442:
  (36, -1, -1) ('[[[[[]]]  [[[[]]]]]  [[[[[[[]]]]]]]]', '((2^3+1)^6+1)')
537824:
  (44, 2, 2) ('[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]  [[[[[[]]]]]]', '14^5')
537825:
  (46, -1, -1) ('[[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]  [[[[[[]]]]]]]', '(14^5+1)')
759375:
  (39, 2, 2) ('[[[[[[[[[]]]]]]]] [[[]]]]  [[[[[[]]]]]]', '(7*2+1)^5')
759376:
  (41, -1, -1) ('[[[[[[[[[[]]]]]]]] [[[]]]]  [[[[[[]]]]]]]', '((7*2+1)^5+1)')
823543:
  (25, 3, 3) ('[[[[[[[[]]]]]]]]   [[[]]]', '7^^2')
  (34, 2, 2) ('[[[[[[[[]]]]]]]]  [[[[[[[[]]]]]]]]', '7^7')
823544:
  (36, -1, -1) ('[[[[[[[[[]]]]]]]]  [[[[[[[[]]]]]]]]]', '(7^7+1)')
1000000:
  (34, 2, 2) ('[[[[[]]]]  [[[]]]]  [[[[[[[]]]]]]]', '(3^2+1)^6')
1000001:
  (36, -1, -1) ('[[[[[[]]]]  [[[]]]]  [[[[[[[]]]]]]]]', '((3^2+1)^6+1)')
1048576:
  (30, 2, 2) ('[[[[[]]]]]  [[[[[]]]]  [[[]]]]', '4^(3^2+1)')
  (31, 2, 3) ('[[[]]]   [[[[]]]]  [[[[[[]]]]]]', '2^^3^5')
1048577:
  (32, -1, -1) ('[[[[[[]]]]]  [[[[[]]]]  [[[]]]]]', '(4^(3^2+1)+1)')
1594323:
  (31, 2, 2) ('[[[[]]]]  [[[[[[]]]]] [[[[]]]]]', '3^(4*3+1)')
1594324:
  (33, -1, -1) ('[[[[[]]]]  [[[[[[]]]]] [[[[]]]]]]', '(3^(4*3+1)+1)')
1679616:
  (34, 2, 2) ('[[[[[[[]]]]]]]  [[[[[[[[[]]]]]]]]]', '6^8')
1679617:
  (36, -1, -1) ('[[[[[[[[]]]]]]]  [[[[[[[[[]]]]]]]]]]', '(6^8+1)')
1771561:
  (37, 2, 2) ('[[[[[[[]]]]]] [[[]]]]  [[[[[[[]]]]]]]', '(5*2+1)^6')
1771562:
  (39, -1, -1) ('[[[[[[[[]]]]]] [[[]]]]  [[[[[[[]]]]]]]]', '((5*2+1)^6+1)')
1953125:
  (32, 2, 2) ('[[[[[[]]]]]]  [[[[]]]  [[[[]]]]]', '5^(2^3+1)')
1953126:
  (34, -1, -1) ('[[[[[[[]]]]]]  [[[[]]]  [[[[]]]]]]', '(5^(2^3+1)+1)')
2097152:
  (36, 2, 2) ('[[[[[[[[[]]]]]]]]]  [[[[[[[[]]]]]]]]', '8^7')
2097153:
  (38, -1, -1) ('[[[[[[[[[[]]]]]]]]]  [[[[[[[[]]]]]]]]]', '(8^7+1)')
2985984:
  (42, 2, 2) ('[[[[[[[[[[[[[]]]]]]]]]]]]]  [[[[[[[]]]]]]]', '12^6')
2985985:
  (44, -1, -1) ('[[[[[[[[[[[[[[]]]]]]]]]]]]]  [[[[[[[]]]]]]]]', '(12^6+1)')
4194304:
  (33, 2, 2) ('[[[[[]]]]]  [[[[[[[]]]]]] [[[]]]]', '4^(5*2+1)')
4194305:
  (35, -1, -1) ('[[[[[[]]]]]  [[[[[[[]]]]]] [[[]]]]]', '(4^(5*2+1)+1)')
4782969:
  (36, 2, 2) ('[[[[]]]  [[[[]]]]]  [[[[[[[[]]]]]]]]', '(2^3+1)^7')
4782970:
  (38, -1, -1) ('[[[[[]]]  [[[[]]]]]  [[[[[[[[]]]]]]]]]', '((2^3+1)^7+1)')
4826809:
  (37, 2, 2) ('[[[[[[]]]]] [[[[]]]]]  [[[[[[[]]]]]]]', '(4*3+1)^6')
4826810:
  (39, -1, -1) ('[[[[[[[]]]]] [[[[]]]]]  [[[[[[[]]]]]]]]', '((4*3+1)^6+1)')
5764801:
  (36, 2, 2) ('[[[[[[[[]]]]]]]]  [[[[[[[[[]]]]]]]]]', '7^8')
5764802:
  (38, -1, -1) ('[[[[[[[[[]]]]]]]]  [[[[[[[[[]]]]]]]]]]', '(7^8+1)')
7529536:
  (46, 2, 2) ('[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]  [[[[[[[]]]]]]]', '14^6')
7529537:
  (48, -1, -1) ('[[[[[[[[[[[[[[[[]]]]]]]]]]]]]]]  [[[[[[[]]]]]]]]', '(14^6+1)')
9765625:
  (32, 2, 2) ('[[[[[[]]]]]]  [[[[[]]]]  [[[]]]]', '5^(3^2+1)')
9765626:
  (34, -1, -1) ('[[[[[[[]]]]]]  [[[[[]]]]  [[[]]]]]', '(5^(3^2+1)+1)')
10000000:
  (36, 2, 2) ('[[[[[]]]]  [[[]]]]  [[[[[[[[]]]]]]]]', '(3^2+1)^7')
10000001:
  (38, -1, -1) ('[[[[[[]]]]  [[[]]]]  [[[[[[[[]]]]]]]]]', '((3^2+1)^7+1)')
10077696:
  (34, 2, 2) ('[[[[[[[]]]]]]]  [[[[]]]  [[[[]]]]]', '6^(2^3+1)')
10077697:
  (36, -1, -1) ('[[[[[[[[]]]]]]]  [[[[]]]  [[[[]]]]]]', '(6^(2^3+1)+1)')
11390625:
  (41, 2, 2) ('[[[[[[[[[]]]]]]]] [[[]]]]  [[[[[[[]]]]]]]', '(7*2+1)^6')
11390626:
  (43, -1, -1) ('[[[[[[[[[[]]]]]]]] [[[]]]]  [[[[[[[]]]]]]]]', '((7*2+1)^6+1)')
14348907:
  (35, 2, 2) ('[[[[]]]]  [[[[[[[[[]]]]]]]] [[[]]]]', '3^(7*2+1)')
14348908:
  (37, -1, -1) ('[[[[[]]]]  [[[[[[[[[]]]]]]]] [[[]]]]]', '(3^(7*2+1)+1)')
16777216:
  (27, 3, 3) ('[[[[[[[[[]]]]]]]]]   [[[]]]', '8^^2')
  (33, 2, 3) ('[[[]]]   [[[[]]]]  [[[[[[[]]]]]]]', '2^^3^6')
  (38, 2, 2) ('[[[[[[[[[]]]]]]]]]  [[[[[[[[[]]]]]]]]]', '8^8')
16777217:
  (35, -1, -1) ('[[[[]]]   [[[[]]]]  [[[[[[[]]]]]]]]', '(2^^3^6+1)')
19487171:
  (39, 2, 2) ('[[[[[[[]]]]]] [[[]]]]  [[[[[[[[]]]]]]]]', '(5*2+1)^7')
19487172:
  (41, -1, -1) ('[[[[[[[[]]]]]] [[[]]]]  [[[[[[[[]]]]]]]]]', '((5*2+1)^7+1)')
35831808:
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100000000:
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170859376:
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214358882:
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362797057:
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387420490:
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815730721:
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815730722:
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1000000000:
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1000000001:
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1073741824:
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1073741825:
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1220703126:
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1475789056:
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1475789057:
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1977326743:
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1977326744:
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