# Square Form Factorization
# Jason E Gower and Samuel S Wagstaff Jr
# AMS Mathematics of Computation
# Volume 77, Number 261, January 2008, Pages 551-588
# S 0025-5718(07)02010-8
# http://homes.cerias.purdue.edu/~ssw/squfof.pdf
# Algorithm 3.3 SQUFOF (continued fraction method)

# see also
# SQUFOF notes by Daniel Shanks
# collected by Steve McMath
# http://www.usna.edu/Users/math/wdj/_files/
#     documents/mcmath/shanks_squfof.pdf

# note the typo in Gower and Wagstaff section 5.2
# in the description of step 2.b which should read
#     put (g, P mod g) onto the QUEUE
# instead of
#     put (g, B mod g) onto the QUEUE

verbose = True

def squfof(n, m=1): # with optional multiplier
    # useful multipliers are 3, 5, 7, 11, 15, 21,
    #   33, 35, 55, 77, 105, 165, 231, 385, 1155
    
    def gcd(a, b): # euclid's algorithm
        if b == 0: return a
        return gcd(b, a % b)
    
    def isqrt(n): # newton's method
        x = n; y = (x + 1) // 2
        while y < x:
            x = y; y = (x + n // x) // 2
        return x
    
    def a(i): return 1 if i % 2 == 0 else -1
    
    if n % 2 == 0: return 2
    g = gcd(n, m)
    if g > 1: return g
    
  # 1. Initialise
    
    s = isqrt(n)
    if s * s == n: return s
    
    d = 2 * m * n if (m * n) % 4 == 1 else m * n
    s = isqrt(d)
    qHat = 1
    p = s
    q = d - p * p
    ell = 2 * isqrt(2 * isqrt(d))
    b = 2 * ell
    i = 0
    queue = []
    
    if verbose:
        print "n =", n
        print "d =", d
        print "s =", s
        print "ell =", ell
        print "b =", b
        print "-------------------------"
        print 0, -1*q, p, 1, queue
    
  # 2. Cycle forward to find a proper square form:
    
    while True:
        
        if verbose: print i+1, a(i)*qHat, p, -1*a(i)*q, queue
        
        # 2a
        littleQ = (s + p) // q
        pPrime = littleQ * q - p
        
        # 2b
        g = q / gcd(q, 2 * m)
        if g <= ell:
            queue.append(g)
            queue.append(p % g)
        
        # 2c
        t = qHat + littleQ * (p - pPrime)
        qHat = q
        q = t
        p = pPrime
        
        # 2d
        if i % 2 == 0:
            
            r = isqrt(q)
            if r * r == q:
                
                z = 0
                while z < len(queue):
                    if r == queue[z] and \
                       (p - queue[z+1]) % r == 0:
                        break
                    z = z + 2
                    
                if z < len(queue):
                    if r > 1:
                        queue = queue[z+2:]
                    elif r == 1:
                        return 0 # square form doesn't exist
                else: break # go to step 3
                
        # 2e
        i = i + 1
        if i > b:
            return 0 # timeout
        
  # 3. Compute an inverse square root of the square form:
    
    if verbose: print i+2, -1*a(i)*qHat, p, a(i)*q, queue
    if verbose: print "-------------------------"
    
    qHat = r
    p = p + r * ((s - p) // r)
    q = (d - p * p) / qHat
    
    if verbose: print 0, -1*a(i)*qHat, p, a(i)*q
    
  # 4. Cycle in the reverse direction to find a factor of N:
    
    for i in range(1, b):
        
        # 4a
        littleQ = (s + p) // q
        pPrime = littleQ * q - p
        
        # 4b
        if p == pPrime: break
        
        # 4c
        t = qHat + littleQ * (p - pPrime)
        qHat = q
        q = t
        p = pPrime
    
        if verbose: print i, -1*a(i)*qHat, p, a(i)*q
        
  # 5. Print the factor of N:
    
    if verbose: print i, -1*a(i)*q, p, a(i)*qHat
    if verbose: print "-------------------------"
    
    q = q / gcd(q, 2 * m)
    return q

print squfof(42854447)

n = 42854447
d = 42854447
s = 6546
ell = 228
b = 456
-------------------------
0 -4331 6546 1 []
1 1 6546 -4331 []
2 -4331 6447 298 []
3 298 6367 -7771 [149, 40]
4 -7771 1404 5261 [149, 40]
5 5261 3857 -5318 [149, 40]
6 -5318 1461 7657 [149, 40]
7 7657 6196 -583 [149, 40]
8 -583 6047 10786 [149, 40]
9 10786 4739 -1891 [149, 40]
10 -1891 4716 10901 [149, 40]
11 10901 6185 -422 [149, 40]
12 -422 6475 2201 [149, 40, 211, 66]
13 2201 4530 -10147 [149, 40, 211, 66]
14 -10147 5617 1114 [149, 40, 211, 66]
15 1114 5523 -11087 [149, 40, 211, 66]
16 -11087 5564 1073 [149, 40, 211, 66]
17 1073 6239 -3662 [149, 40, 211, 66]
18 -3662 4747 5549 [149, 40, 211, 66]
19 5549 6351 -454 [149, 40, 211, 66]
20 -454 6361 5269 [149, 40, 211, 66, 227, 222]
21 5269 4177 -4822 [149, 40, 211, 66, 227, 222]
22 -4822 5467 2689 [149, 40, 211, 66, 227, 222]
23 2689 5289 -5534 [149, 40, 211, 66, 227, 222]
24 -5534 5779 1709 [149, 40, 211, 66, 227, 222]
25 1709 6184 -2699 [149, 40, 211, 66, 227, 222]
26 -2699 4612 7997 [149, 40, 211, 66, 227, 222]
27 7997 3385 -3926 [149, 40, 211, 66, 227, 222]
28 -3926 4467 5833 [149, 40, 211, 66, 227, 222]
29 5833 1366 -7027 [149, 40, 211, 66, 227, 222]
30 -7027 5661 1538 [149, 40, 211, 66, 227, 222]
31 1538 5105 -10919 [149, 40, 211, 66, 227, 222]
32 -10919 5814 829 [149, 40, 211, 66, 227, 222]
33 829 5792 -11227 [149, 40, 211, 66, 227, 222]
34 -11227 5435 1186 [149, 40, 211, 66, 227, 222]
35 1186 6425 -1327 [149, 40, 211, 66, 227, 222]
36 -1327 5518 9349 [149, 40, 211, 66, 227, 222]
37 9349 3831 -3014 [149, 40, 211, 66, 227, 222]
38 -3014 5211 5209 [149, 40, 211, 66, 227, 222]
39 5209 5207 -3022 [149, 40, 211, 66, 227, 222]
40 -3022 3859 9253 [149, 40, 211, 66, 227, 222]
41 9253 5394 -1487 [149, 40, 211, 66, 227, 222]
42 -1487 6502 389 [149, 40, 211, 66, 227, 222]
43 389 6335 -6998 [149, 40, 211, 66, 227, 222]
44 -6998 663 6061 [149, 40, 211, 66, 227, 222]
45 6061 5398 -2263 [149, 40, 211, 66, 227, 222]
46 -2263 5917 3466 [149, 40, 211, 66, 227, 222]
47 3466 4481 -6571 [149, 40, 211, 66, 227, 222]
48 -6571 2090 5857 [149, 40, 211, 66, 227, 222]
49 5857 3767 -4894 [149, 40, 211, 66, 227, 222]
50 -4894 6021 1349 [149, 40, 211, 66, 227, 222]
51 1349 6120 -4003 [149, 40, 211, 66, 227, 222]
52 -4003 5889 2042 [149, 40, 211, 66, 227, 222]
53 2042 6363 -1159 [149, 40, 211, 66, 227, 222]
54 -1159 6386 1789 [149, 40, 211, 66, 227, 222]
55 1789 6137 -2902 [149, 40, 211, 66, 227, 222]
56 -2902 5471 4453 [149, 40, 211, 66, 227, 222]
57 4453 3435 -6974 [149, 40, 211, 66, 227, 222]
58 -6974 3539 4349 [149, 40, 211, 66, 227, 222]
59 4349 5159 -3734 [149, 40, 211, 66, 227, 222]
60 -3734 6043 1697 [149, 40, 211, 66, 227, 222]
61 1697 5836 -5183 [149, 40, 211, 66, 227, 222]
62 -5183 4530 4309 [149, 40, 211, 66, 227, 222]
63 4309 4088 -6067 [149, 40, 211, 66, 227, 222]
64 -6067 1979 6418 [149, 40, 211, 66, 227, 222]
65 6418 4439 -3607 [149, 40, 211, 66, 227, 222]
66 -3607 6382 589 [149, 40, 211, 66, 227, 222]
67 589 5987 -11902 [149, 40, 211, 66, 227, 222]
68 -11902 5915 661 [149, 40, 211, 66, 227, 222]
69 661 5983 -10678 [149, 40, 211, 66, 227, 222]
70 -10678 4695 1949 [149, 40, 211, 66, 227, 222]
71 1949 5050 -8903 [149, 40, 211, 66, 227, 222]
72 -8903 3853 3146 [149, 40, 211, 66, 227, 222]
73 3146 5585 -3707 [149, 40, 211, 66, 227, 222]
74 -3707 5536 3293 [149, 40, 211, 66, 227, 222]
75 3293 4343 -7286 [149, 40, 211, 66, 227, 222]
76 -7286 2943 4693 [149, 40, 211, 66, 227, 222]
77 4693 6443 -286 [149, 40, 211, 66, 227, 222]
78 -286 6427 5413 [149, 40, 211, 66, 227, 222, 143, 8]
79 5413 4399 -4342 [149, 40, 211, 66, 227, 222, 143, 8]
80 -4342 4285 5641 [149, 40, 211, 66, 227, 222, 143, 8]
81 5641 1356 -7271 [149, 40, 211, 66, 227, 222, 143, 8]
82 -7271 5915 1082 [149, 40, 211, 66, 227, 222, 143, 8]
83 1082 5987 -6479 [149, 40, 211, 66, 227, 222, 143, 8]
84 -6479 492 6577 [149, 40, 211, 66, 227, 222, 143, 8]
85 6577 6085 -886 [149, 40, 211, 66, 227, 222, 143, 8]
86 -886 6319 3301 [149, 40, 211, 66, 227, 222, 143, 8]
87 3301 3584 -9091 [149, 40, 211, 66, 227, 222, 143, 8]
88 -9091 5507 1378 [149, 40, 211, 66, 227, 222, 143, 8]
89 1378 5517 -9011 [149, 40, 211, 66, 227, 222, 143, 8]
90 -9011 3494 3401 [149, 40, 211, 66, 227, 222, 143, 8]
91 3401 3308 -9383 [149, 40, 211, 66, 227, 222, 143, 8]
92 -9383 6075 634 [149, 40, 211, 66, 227, 222, 143, 8]
93 634 5971 -11359 [149, 40, 211, 66, 227, 222, 143, 8]
94 -11359 5388 1217 [149, 40, 211, 66, 227, 222, 143, 8]
95 1217 5565 -9766 [149, 40, 211, 66, 227, 222, 143, 8]
96 -9766 4201 2581 [149, 40, 211, 66, 227, 222, 143, 8]
97 2581 6123 -2078 [149, 40, 211, 66, 227, 222, 143, 8]
98 -2078 6345 1249 [149, 40, 211, 66, 227, 222, 143, 8]
99 1249 6145 -4078 [149, 40, 211, 66, 227, 222, 143, 8]
100 -4078 6089 1417 [149, 40, 211, 66, 227, 222, 143, 8]
101 1417 5247 -10814 [149, 40, 211, 66, 227, 222, 143, 8]
102 -10814 5567 1097 [149, 40, 211, 66, 227, 222, 143, 8]
103 1097 6500 -551 [149, 40, 211, 66, 227, 222, 143, 8]
104 -551 6173 8618 [149, 40, 211, 66, 227, 222, 143, 8]
105 8618 2445 -4279 [149, 40, 211, 66, 227, 222, 143, 8]
106 -4279 6113 1282 [149, 40, 211, 66, 227, 222, 143, 8]
107 1282 5425 -10471 [149, 40, 211, 66, 227, 222, 143, 8]
108 -10471 5046 1661 [149, 40, 211, 66, 227, 222, 143, 8]
109 1661 4920 -11227 [149, 40, 211, 66, 227, 222, 143, 8]
110 -11227 6307 274 [149, 40, 211, 66, 227, 222, 143, 8]
111 274 6297 -11687 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
112 -11687 5390 1181 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
113 1181 6420 -1387 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
114 -1387 6063 4394 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
115 4394 2725 -8063 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
116 -8063 5338 1781 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
117 1781 5348 -8003 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
118 -8003 2655 4474 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
119 4474 6293 -727 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
120 -727 6066 8333 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
121 8333 2267 -4526 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
122 -4526 2259 8341 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
123 8341 6082 -703 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
124 -703 5869 11962 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
125 11962 6093 -479 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
126 -479 6361 4994 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
127 4994 3627 -5947 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
128 -5947 2320 6301 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
129 6301 3981 -4286 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
130 -4286 4591 5081 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
131 5081 5571 -2326 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
132 -2326 6059 2641 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
133 2641 4505 -8542 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
134 -8542 4037 3109 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
135 3109 5290 -4783 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
136 -4783 4276 5137 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
137 5137 5998 -1339 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
138 -1339 6053 4642 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
139 4642 3231 -6983 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
140 -6983 3752 4121 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
141 4121 4490 -5507 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
142 -5507 6524 53 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5]
143 53 6514 -7967 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5]
144 -7967 1453 5114 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5]
145 5114 3661 -5759 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5]
146 -5759 2098 6677 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5]
147 6677 4579 -3278 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5]
148 -3278 5255 4649 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5]
149 4649 4043 -5702 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5]
150 -5702 1659 7033 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5]
151 7033 5374 -1987 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5]
152 -1987 4561 11098 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5]
153 11098 6537 -11 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5]
154 -11 6542 5153 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
155 5153 3764 -5567 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
156 -5567 1803 7114 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
157 7114 5311 -2059 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
158 -2059 4984 8749 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
159 8749 3765 -3278 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
160 -3278 6069 1837 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
161 1837 4953 -9974 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
162 -9974 5021 1769 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
163 1769 5593 -6542 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
164 -6542 949 6413 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
165 6413 5464 -2027 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
166 -2027 4671 10378 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
167 10378 5707 -991 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
168 -991 6185 4642 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
169 4642 3099 -7163 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
170 -7163 4064 3677 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
171 3677 3290 -8711 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
172 -8711 5421 1546 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
173 1546 5401 -8851 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
174 -8851 3450 3497 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
175 3497 3544 -8663 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
176 -8663 5119 1922 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
177 1922 6413 -899 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
178 -899 6173 5282 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
179 5282 4391 -4463 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
180 -4463 4535 4994 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
181 4994 5453 -2627 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
182 -2627 5055 6586 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
183 6586 1531 -6151 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
184 -6151 4620 3497 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
185 3497 5871 -2398 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
186 -2398 6119 2257 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
187 2257 5166 -7163 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
188 -7163 1997 5426 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
189 5426 3429 -5731 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
190 -5731 2302 6553 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
191 6553 4251 -3782 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
192 -3782 3313 8429 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
193 8429 5116 -1979 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
194 -1979 4779 10114 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
195 10114 5335 -1423 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
196 -1423 6049 4402 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
197 4402 2755 -8011 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
198 -8011 5256 1901 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
199 1901 6150 -2647 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
200 -2647 4438 8749 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
201 8749 4311 -2774 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
202 -2774 4011 9649 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
203 9649 5638 -1147 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
204 -1147 5832 7709 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
205 7709 1877 -5102 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
206 -5102 3225 6361 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
207 6361 3136 -5191 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
208 -5191 2055 7442 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
209 7442 5387 -1859 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
210 -1859 5767 5162 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
211 5162 4557 -4279 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
212 -4279 4001 6274 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
213 6274 2273 -6007 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
214 -6007 3734 4813 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
215 4813 5892 -1691 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
216 -1691 5945 4442 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
217 4442 2939 -7703 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
218 -7703 4764 2617 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
219 2617 5704 -3943 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
220 -3943 6125 1354 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
221 1354 6061 -4519 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
222 -4519 2977 7522 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
223 7522 4545 -2951 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
224 -2951 4308 8233 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
225 8233 3925 -3334 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
226 -3334 6077 1777 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
227 1777 6362 -1339 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
228 -1339 5689 7834 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
229 7834 2145 -4883 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
230 -4883 2738 7241 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
231 7241 4503 -3118 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
232 -3118 4851 6197 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
233 6197 1346 -6623 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
234 -6623 5277 2266 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
235 2266 6053 -2743 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
236 -2743 4919 6802 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
237 6802 1883 -5779 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
238 -5779 3896 4789 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
239 4789 5682 -2207 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
240 -2207 5353 6434 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
241 6434 1081 -6479 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
242 -6479 5398 2117 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
243 2117 5187 -7534 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
244 -7534 2347 4957 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
245 4957 2610 -7271 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
246 -7271 4661 2906 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
247 2906 4057 -9083 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
248 -9083 5026 1937 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
249 1937 4659 -10918 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
250 -10918 6259 337 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
251 337 6210 -12731 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
252 -12731 6521 26 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3]
253 26 6531 -7711 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
254 -7711 1180 5377 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
255 5377 4197 -4694 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
256 -4694 5191 3389 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
257 3389 4976 -5339 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
258 -5339 5702 1937 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
259 1937 5920 -4031 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
260 -4031 6173 1178 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
261 1178 5607 -9691 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
262 -9691 4084 2701 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
263 2701 4019 -9886 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
264 -9886 5867 853 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
265 853 6075 -6974 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
266 -6974 899 6029 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
267 6029 5130 -2743 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
268 -2743 5842 3181 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
269 3181 3701 -9166 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
270 -9166 5465 1417 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
271 1417 5871 -5918 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
272 -5918 5965 1229 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
273 1229 6325 -2318 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
274 -2318 5265 6529 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
275 6529 1264 -6319 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
276 -6319 5055 2738 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
277 2738 5897 -2951 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
278 -2951 5907 2698 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
279 2698 4885 -7039 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
280 -7039 2154 5429 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
281 5429 3275 -5918 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
282 -5918 2643 6061 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
283 6061 3418 -5143 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
284 -5143 1725 7754 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
285 7754 6029 -839 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
286 -839 5717 12122 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
287 12122 6405 -151 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8]
288 -151 6430 9997 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
289 9997 3567 -3014 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
290 -3014 5475 4273 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
291 4273 3071 -7822 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
292 -7822 4751 2593 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
293 2593 5621 -4342 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
294 -4342 3063 7709 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
295 7709 4646 -2759 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
296 -2759 6390 733 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
297 733 6071 -8182 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
298 -8182 2111 4693 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
299 4693 2582 -7711 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
300 -7711 5129 2146 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
301 2146 5601 -5351 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
302 -5351 5101 3146 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
303 3146 4337 -7643 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
304 -7643 3306 4177 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
305 4177 5048 -4159 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
306 -4159 3270 7733 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
307 7733 4463 -2966 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
308 -2966 4435 7817 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
309 7817 3382 -4019 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
310 -4019 4656 5269 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
311 5269 5882 -1567 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
312 -1567 5087 10834 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
313 10834 5747 -907 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
314 -907 6044 6973 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
315 6973 929 -6022 [149, 40, 211, 66, 227, 222, 143, 8, 137, 5, 53, 5, 11, 3, 13, 8, 151, 63]
316 -6022 5093 2809 [11, 3, 13, 8, 151, 63]
317 2809 6143 -1822 [11, 3, 13, 8, 151, 63]
318 -1822 4789 10933 [11, 3, 13, 8, 151, 63]
319 10933 6144 -467 [11, 3, 13, 8, 151, 63]
320 -467 6465 2266 [11, 3, 13, 8, 151, 63]
321 2266 4865 -8467 [11, 3, 13, 8, 151, 63]
322 -8467 3602 3529 [11, 3, 13, 8, 151, 63]
323 3529 3456 -8759 [11, 3, 13, 8, 151, 63]
324 -8759 5303 1682 [11, 3, 13, 8, 151, 63]
325 1682 6471 -583 [11, 3, 13, 8, 151, 63]
326 -583 6355 4234 [11, 3, 13, 8, 151, 63]
327 4234 6347 -607 [11, 3, 13, 8, 151, 63]
328 -607 6400 3121 [11, 3, 13, 8, 151, 63]
329 3121 6084 -1871 [11, 3, 13, 8, 151, 63]
330 -1871 5142 8773 [11, 3, 13, 8, 151, 63]
331 8773 3631 -3382 [11, 3, 13, 8, 151, 63]
332 -3382 6515 121 [13, 8, 151, 63]
333 121 6432 -12263 [13, 8, 151, 63, 121, 102]
334 -12263 5831 722 [13, 8, 151, 63, 121, 102]
335 722 6443 -1859 [13, 8, 151, 63, 121, 102]
336 -1859 4711 11114 [13, 8, 151, 63, 121, 102]
337 11114 6403 -167 [13, 8, 151, 63, 121, 102]
338 -167 6456 7033 [13, 8, 151, 63, 121, 102, 167, 57]
339 7033 577 -6046 [13, 8, 151, 63, 121, 102, 167, 57]
340 -6046 5469 2141 [13, 8, 151, 63, 121, 102, 167, 57]
341 2141 5236 -7211 [13, 8, 151, 63, 121, 102, 167, 57]
342 -7211 1975 5402 [13, 8, 151, 63, 121, 102, 167, 57]
343 5402 3427 -5759 [13, 8, 151, 63, 121, 102, 167, 57]
344 -5759 2332 6497 [13, 8, 151, 63, 121, 102, 167, 57]
345 6497 4165 -3926 [13, 8, 151, 63, 121, 102, 167, 57]
346 -3926 3687 7453 [13, 8, 151, 63, 121, 102, 167, 57]
347 7453 3766 -3847 [13, 8, 151, 63, 121, 102, 167, 57]
348 -3847 3928 7129 [13, 8, 151, 63, 121, 102, 167, 57]
349 7129 3201 -4574 [13, 8, 151, 63, 121, 102, 167, 57]
350 -4574 5947 1637 [13, 8, 151, 63, 121, 102, 167, 57]
351 1637 5512 -7619 [13, 8, 151, 63, 121, 102, 167, 57]
352 -7619 2107 5042 [13, 8, 151, 63, 121, 102, 167, 57]
353 5042 2935 -6791 [13, 8, 151, 63, 121, 102, 167, 57]
354 -6791 3856 4121 [13, 8, 151, 63, 121, 102, 167, 57]
355 4121 4386 -5731 [13, 8, 151, 63, 121, 102, 167, 57]
356 -5731 1345 7162 [13, 8, 151, 63, 121, 102, 167, 57]
357 7162 5817 -1259 [13, 8, 151, 63, 121, 102, 167, 57]
358 -1259 5514 9889 [13, 8, 151, 63, 121, 102, 167, 57]
359 9889 4375 -2398 [13, 8, 151, 63, 121, 102, 167, 57]
360 -2398 5217 6521 [13, 8, 151, 63, 121, 102, 167, 57]
361 6521 1304 -6311 [13, 8, 151, 63, 121, 102, 167, 57]
362 -6311 5007 2818 [13, 8, 151, 63, 121, 102, 167, 57]
363 2818 6265 -1279 [13, 8, 151, 63, 121, 102, 167, 57]
364 -1279 6525 218 [13, 8, 151, 63, 121, 102, 167, 57]
365 218 6337 -12371 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
366 -12371 6034 521 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
367 521 6470 -1907 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
368 -1907 4972 9509 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
369 9509 4537 -2342 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
370 -2342 4831 8333 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
371 8333 3502 -3671 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
372 -3671 3840 7657 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
373 7657 3817 -3694 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
374 -3694 3571 8149 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
375 8149 4578 -2687 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
376 -2687 6170 1781 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
377 1781 6297 -1798 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
378 -1798 6289 1837 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
379 1837 4733 -11134 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
380 -11134 6401 169 [13, 8, 151, 63, 121, 102, 167, 57, 109, 94]
-------------------------
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172 -2633 4423 8846
173 8846 4423 -2633
-------------------------
4423