<p>Given a non-negative integer <code>c</code>, decide whether there&#39;re two integers <code>a</code> and <code>b</code> such that <code>a<sup>2</sup> + b<sup>2</sup> = c</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> c = 5
<strong>Output:</strong> true
<strong>Explanation:</strong> 1 * 1 + 2 * 2 = 5
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> c = 3
<strong>Output:</strong> false
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= c &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

import math
from collections import Counter


class Solution:
    def __init__(self):
        """The sum of squares theorem states that any integer larger than 1
        can be written as a sum of two squares if and only if its prime
        decomposition contains no factors p ** k where p is congruent to
        3 mod 4 and k is odd.  To efficiently calulate the prime
        decomposition of c, this solution uses a precomputed list of all
        primes up to the square root of the largest input possible.
        """
        self.primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 
            31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 
            73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 
            127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 
            179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 
            233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 
            283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 
            353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 
            419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 
            467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 
            547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 
            607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 
            661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 
            739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 
            811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 
            877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 
            947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 
            1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 
            1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 
            1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 
            1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 
            1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 
            1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 
            1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 
            1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 
            1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 
            1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 
            1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 
            1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 
            1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 
            1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 
            2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 
            2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 
            2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 
            2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 
            2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 
            2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 
            2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 
            2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 
            2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 
            2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 
            2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 
            2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 
            3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 
            3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 
            3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 
            3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 
            3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 
            3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 
            3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 
            3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 
            3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 
            3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 
            3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 
            3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 
            4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 
            4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 
            4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 
            4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 
            4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 
            4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 
            4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 
            4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 
            4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 
            4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 
            4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 
            4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 
            5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 
            5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 
            5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 
            5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 
            5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 
            5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 
            5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 
            5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 
            5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 
            5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 
            5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 
            5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 
            6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 
            6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 
            6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 
            6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 
            6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 
            6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 
            6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 
            6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 
            6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 
            6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 
            6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 
            7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 
            7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 
            7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 
            7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 
            7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 
            7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 
            7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 
            7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 
            7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 
            7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 
            7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 
            8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 
            8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 
            8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 
            8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 
            8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 
            8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 
            8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 
            8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 
            8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 
            8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 
            8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 
            9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 
            9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 
            9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 
            9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 
            9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 
            9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 
            9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 
            9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 
            9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 
            9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 
            9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 
            10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 
            10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 
            10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, 
            10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, 
            10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, 
            10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 
            10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657, 
            10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, 
            10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 
            10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 
            10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 
            11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 
            11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251, 
            11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, 
            11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, 
            11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, 
            11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, 
            11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, 
            11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, 
            11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 
            11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 
            12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 
            12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 
            12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, 
            12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, 
            12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, 
            12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 
            12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, 
            12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, 
            12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, 
            12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 
            12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 
            13009, 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 
            13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, 
            13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, 
            13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, 
            13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499, 
            13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597, 13613, 13619, 
            13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697, 
            13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, 13781, 
            13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879, 
            13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967, 
            13997, 13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 
            14083, 14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 
            14207, 14221, 14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 
            14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407, 14411, 14419, 
            14423, 14431, 14437, 14447, 14449, 14461, 14479, 14489, 14503, 14519, 
            14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593, 
            14621, 14627, 14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699, 
            14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753, 14759, 14767, 
            14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, 14843, 14851, 
            14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947, 
            14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, 
            15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 
            15161, 15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 
            15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 
            15329, 15331, 15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401, 
            15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473, 15493, 15497, 
            15511, 15527, 15541, 15551, 15559, 15569, 15581, 15583, 15601, 15607, 
            15619, 15629, 15641, 15643, 15647, 15649, 15661, 15667, 15671, 15679, 
            15683, 15727, 15731, 15733, 15737, 15739, 15749, 15761, 15767, 15773, 
            15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, 15877, 15881, 
            15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959, 15971, 
            15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, 
            16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 
            16187, 16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 
            16273, 16301, 16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381, 
            16411, 16417, 16421, 16427, 16433, 16447, 16451, 16453, 16477, 16481, 
            16487, 16493, 16519, 16529, 16547, 16553, 16561, 16567, 16573, 16603, 
            16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661, 16673, 16691, 
            16693, 16699, 16703, 16729, 16741, 16747, 16759, 16763, 16787, 16811, 
            16823, 16829, 16831, 16843, 16871, 16879, 16883, 16889, 16901, 16903, 
            16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981, 16987, 16993, 
            17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, 17093, 
            17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, 
            17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299, 17317, 
            17321, 17327, 17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389, 
            17393, 17401, 17417, 17419, 17431, 17443, 17449, 17467, 17471, 17477, 
            17483, 17489, 17491, 17497, 17509, 17519, 17539, 17551, 17569, 17573, 
            17579, 17581, 17597, 17599, 17609, 17623, 17627, 17657, 17659, 17669, 
            17681, 17683, 17707, 17713, 17729, 17737, 17747, 17749, 17761, 17783, 
            17789, 17791, 17807, 17827, 17837, 17839, 17851, 17863, 17881, 17891, 
            17903, 17909, 17911, 17921, 17923, 17929, 17939, 17957, 17959, 17971, 
            17977, 17981, 17987, 17989, 18013, 18041, 18043, 18047, 18049, 18059, 
            18061, 18077, 18089, 18097, 18119, 18121, 18127, 18131, 18133, 18143, 
            18149, 18169, 18181, 18191, 18199, 18211, 18217, 18223, 18229, 18233, 
            18251, 18253, 18257, 18269, 18287, 18289, 18301, 18307, 18311, 18313, 
            18329, 18341, 18353, 18367, 18371, 18379, 18397, 18401, 18413, 18427, 
            18433, 18439, 18443, 18451, 18457, 18461, 18481, 18493, 18503, 18517, 
            18521, 18523, 18539, 18541, 18553, 18583, 18587, 18593, 18617, 18637, 
            18661, 18671, 18679, 18691, 18701, 18713, 18719, 18731, 18743, 18749, 
            18757, 18773, 18787, 18793, 18797, 18803, 18839, 18859, 18869, 18899, 
            18911, 18913, 18917, 18919, 18947, 18959, 18973, 18979, 19001, 19009, 
            19013, 19031, 19037, 19051, 19069, 19073, 19079, 19081, 19087, 19121, 
            19139, 19141, 19157, 19163, 19181, 19183, 19207, 19211, 19213, 19219, 
            19231, 19237, 19249, 19259, 19267, 19273, 19289, 19301, 19309, 19319, 
            19333, 19373, 19379, 19381, 19387, 19391, 19403, 19417, 19421, 19423, 
            19427, 19429, 19433, 19441, 19447, 19457, 19463, 19469, 19471, 19477, 
            19483, 19489, 19501, 19507, 19531, 19541, 19543, 19553, 19559, 19571, 
            19577, 19583, 19597, 19603, 19609, 19661, 19681, 19687, 19697, 19699, 
            19709, 19717, 19727, 19739, 19751, 19753, 19759, 19763, 19777, 19793, 
            19801, 19813, 19819, 19841, 19843, 19853, 19861, 19867, 19889, 19891, 
            19913, 19919, 19927, 19937, 19949, 19961, 19963, 19973, 19979, 19991, 
            19993, 19997, 20011, 20021, 20023, 20029, 20047, 20051, 20063, 20071, 
            20089, 20101, 20107, 20113, 20117, 20123, 20129, 20143, 20147, 20149, 
            20161, 20173, 20177, 20183, 20201, 20219, 20231, 20233, 20249, 20261, 
            20269, 20287, 20297, 20323, 20327, 20333, 20341, 20347, 20353, 20357, 
            20359, 20369, 20389, 20393, 20399, 20407, 20411, 20431, 20441, 20443, 
            20477, 20479, 20483, 20507, 20509, 20521, 20533, 20543, 20549, 20551, 
            20563, 20593, 20599, 20611, 20627, 20639, 20641, 20663, 20681, 20693, 
            20707, 20717, 20719, 20731, 20743, 20747, 20749, 20753, 20759, 20771, 
            20773, 20789, 20807, 20809, 20849, 20857, 20873, 20879, 20887, 20897, 
            20899, 20903, 20921, 20929, 20939, 20947, 20959, 20963, 20981, 20983, 
            21001, 21011, 21013, 21017, 21019, 21023, 21031, 21059, 21061, 21067, 
            21089, 21101, 21107, 21121, 21139, 21143, 21149, 21157, 21163, 21169, 
            21179, 21187, 21191, 21193, 21211, 21221, 21227, 21247, 21269, 21277, 
            21283, 21313, 21317, 21319, 21323, 21341, 21347, 21377, 21379, 21383, 
            21391, 21397, 21401, 21407, 21419, 21433, 21467, 21481, 21487, 21491, 
            21493, 21499, 21503, 21517, 21521, 21523, 21529, 21557, 21559, 21563, 
            21569, 21577, 21587, 21589, 21599, 21601, 21611, 21613, 21617, 21647, 
            21649, 21661, 21673, 21683, 21701, 21713, 21727, 21737, 21739, 21751, 
            21757, 21767, 21773, 21787, 21799, 21803, 21817, 21821, 21839, 21841, 
            21851, 21859, 21863, 21871, 21881, 21893, 21911, 21929, 21937, 21943, 
            21961, 21977, 21991, 21997, 22003, 22013, 22027, 22031, 22037, 22039, 
            22051, 22063, 22067, 22073, 22079, 22091, 22093, 22109, 22111, 22123, 
            22129, 22133, 22147, 22153, 22157, 22159, 22171, 22189, 22193, 22229, 
            22247, 22259, 22271, 22273, 22277, 22279, 22283, 22291, 22303, 22307, 
            22343, 22349, 22367, 22369, 22381, 22391, 22397, 22409, 22433, 22441, 
            22447, 22453, 22469, 22481, 22483, 22501, 22511, 22531, 22541, 22543, 
            22549, 22567, 22571, 22573, 22613, 22619, 22621, 22637, 22639, 22643, 
            22651, 22669, 22679, 22691, 22697, 22699, 22709, 22717, 22721, 22727, 
            22739, 22741, 22751, 22769, 22777, 22783, 22787, 22807, 22811, 22817, 
            22853, 22859, 22861, 22871, 22877, 22901, 22907, 22921, 22937, 22943, 
            22961, 22963, 22973, 22993, 23003, 23011, 23017, 23021, 23027, 23029, 
            23039, 23041, 23053, 23057, 23059, 23063, 23071, 23081, 23087, 23099, 
            23117, 23131, 23143, 23159, 23167, 23173, 23189, 23197, 23201, 23203, 
            23209, 23227, 23251, 23269, 23279, 23291, 23293, 23297, 23311, 23321, 
            23327, 23333, 23339, 23357, 23369, 23371, 23399, 23417, 23431, 23447, 
            23459, 23473, 23497, 23509, 23531, 23537, 23539, 23549, 23557, 23561, 
            23563, 23567, 23581, 23593, 23599, 23603, 23609, 23623, 23627, 23629, 
            23633, 23663, 23669, 23671, 23677, 23687, 23689, 23719, 23741, 23743, 
            23747, 23753, 23761, 23767, 23773, 23789, 23801, 23813, 23819, 23827, 
            23831, 23833, 23857, 23869, 23873, 23879, 23887, 23893, 23899, 23909, 
            23911, 23917, 23929, 23957, 23971, 23977, 23981, 23993, 24001, 24007, 
            24019, 24023, 24029, 24043, 24049, 24061, 24071, 24077, 24083, 24091, 
            24097, 24103, 24107, 24109, 24113, 24121, 24133, 24137, 24151, 24169, 
            24179, 24181, 24197, 24203, 24223, 24229, 24239, 24247, 24251, 24281, 
            24317, 24329, 24337, 24359, 24371, 24373, 24379, 24391, 24407, 24413, 
            24419, 24421, 24439, 24443, 24469, 24473, 24481, 24499, 24509, 24517, 
            24527, 24533, 24547, 24551, 24571, 24593, 24611, 24623, 24631, 24659, 
            24671, 24677, 24683, 24691, 24697, 24709, 24733, 24749, 24763, 24767, 
            24781, 24793, 24799, 24809, 24821, 24841, 24847, 24851, 24859, 24877, 
            24889, 24907, 24917, 24919, 24923, 24943, 24953, 24967, 24971, 24977, 
            24979, 24989, 25013, 25031, 25033, 25037, 25057, 25073, 25087, 25097, 
            25111, 25117, 25121, 25127, 25147, 25153, 25163, 25169, 25171, 25183, 
            25189, 25219, 25229, 25237, 25243, 25247, 25253, 25261, 25301, 25303, 
            25307, 25309, 25321, 25339, 25343, 25349, 25357, 25367, 25373, 25391, 
            25409, 25411, 25423, 25439, 25447, 25453, 25457, 25463, 25469, 25471, 
            25523, 25537, 25541, 25561, 25577, 25579, 25583, 25589, 25601, 25603, 
            25609, 25621, 25633, 25639, 25643, 25657, 25667, 25673, 25679, 25693, 
            25703, 25717, 25733, 25741, 25747, 25759, 25763, 25771, 25793, 25799, 
            25801, 25819, 25841, 25847, 25849, 25867, 25873, 25889, 25903, 25913, 
            25919, 25931, 25933, 25939, 25943, 25951, 25969, 25981, 25997, 25999, 
            26003, 26017, 26021, 26029, 26041, 26053, 26083, 26099, 26107, 26111, 
            26113, 26119, 26141, 26153, 26161, 26171, 26177, 26183, 26189, 26203, 
            26209, 26227, 26237, 26249, 26251, 26261, 26263, 26267, 26293, 26297, 
            26309, 26317, 26321, 26339, 26347, 26357, 26371, 26387, 26393, 26399, 
            26407, 26417, 26423, 26431, 26437, 26449, 26459, 26479, 26489, 26497, 
            26501, 26513, 26539, 26557, 26561, 26573, 26591, 26597, 26627, 26633, 
            26641, 26647, 26669, 26681, 26683, 26687, 26693, 26699, 26701, 26711, 
            26713, 26717, 26723, 26729, 26731, 26737, 26759, 26777, 26783, 26801, 
            26813, 26821, 26833, 26839, 26849, 26861, 26863, 26879, 26881, 26891, 
            26893, 26903, 26921, 26927, 26947, 26951, 26953, 26959, 26981, 26987, 
            26993, 27011, 27017, 27031, 27043, 27059, 27061, 27067, 27073, 27077, 
            27091, 27103, 27107, 27109, 27127, 27143, 27179, 27191, 27197, 27211, 
            27239, 27241, 27253, 27259, 27271, 27277, 27281, 27283, 27299, 27329, 
            27337, 27361, 27367, 27397, 27407, 27409, 27427, 27431, 27437, 27449, 
            27457, 27479, 27481, 27487, 27509, 27527, 27529, 27539, 27541, 27551, 
            27581, 27583, 27611, 27617, 27631, 27647, 27653, 27673, 27689, 27691, 
            27697, 27701, 27733, 27737, 27739, 27743, 27749, 27751, 27763, 27767, 
            27773, 27779, 27791, 27793, 27799, 27803, 27809, 27817, 27823, 27827, 
            27847, 27851, 27883, 27893, 27901, 27917, 27919, 27941, 27943, 27947, 
            27953, 27961, 27967, 27983, 27997, 28001, 28019, 28027, 28031, 28051, 
            28057, 28069, 28081, 28087, 28097, 28099, 28109, 28111, 28123, 28151, 
            28163, 28181, 28183, 28201, 28211, 28219, 28229, 28277, 28279, 28283, 
            28289, 28297, 28307, 28309, 28319, 28349, 28351, 28387, 28393, 28403, 
            28409, 28411, 28429, 28433, 28439, 28447, 28463, 28477, 28493, 28499, 
            28513, 28517, 28537, 28541, 28547, 28549, 28559, 28571, 28573, 28579, 
            28591, 28597, 28603, 28607, 28619, 28621, 28627, 28631, 28643, 28649, 
            28657, 28661, 28663, 28669, 28687, 28697, 28703, 28711, 28723, 28729, 
            28751, 28753, 28759, 28771, 28789, 28793, 28807, 28813, 28817, 28837, 
            28843, 28859, 28867, 28871, 28879, 28901, 28909, 28921, 28927, 28933, 
            28949, 28961, 28979, 29009, 29017, 29021, 29023, 29027, 29033, 29059, 
            29063, 29077, 29101, 29123, 29129, 29131, 29137, 29147, 29153, 29167, 
            29173, 29179, 29191, 29201, 29207, 29209, 29221, 29231, 29243, 29251, 
            29269, 29287, 29297, 29303, 29311, 29327, 29333, 29339, 29347, 29363, 
            29383, 29387, 29389, 29399, 29401, 29411, 29423, 29429, 29437, 29443, 
            29453, 29473, 29483, 29501, 29527, 29531, 29537, 29567, 29569, 29573, 
            29581, 29587, 29599, 29611, 29629, 29633, 29641, 29663, 29669, 29671, 
            29683, 29717, 29723, 29741, 29753, 29759, 29761, 29789, 29803, 29819, 
            29833, 29837, 29851, 29863, 29867, 29873, 29879, 29881, 29917, 29921, 
            29927, 29947, 29959, 29983, 29989, 30011, 30013, 30029, 30047, 30059, 
            30071, 30089, 30091, 30097, 30103, 30109, 30113, 30119, 30133, 30137, 
            30139, 30161, 30169, 30181, 30187, 30197, 30203, 30211, 30223, 30241, 
            30253, 30259, 30269, 30271, 30293, 30307, 30313, 30319, 30323, 30341, 
            30347, 30367, 30389, 30391, 30403, 30427, 30431, 30449, 30467, 30469, 
            30491, 30493, 30497, 30509, 30517, 30529, 30539, 30553, 30557, 30559, 
            30577, 30593, 30631, 30637, 30643, 30649, 30661, 30671, 30677, 30689, 
            30697, 30703, 30707, 30713, 30727, 30757, 30763, 30773, 30781, 30803, 
            30809, 30817, 30829, 30839, 30841, 30851, 30853, 30859, 30869, 30871, 
            30881, 30893, 30911, 30931, 30937, 30941, 30949, 30971, 30977, 30983, 
            31013, 31019, 31033, 31039, 31051, 31063, 31069, 31079, 31081, 31091, 
            31121, 31123, 31139, 31147, 31151, 31153, 31159, 31177, 31181, 31183, 
            31189, 31193, 31219, 31223, 31231, 31237, 31247, 31249, 31253, 31259, 
            31267, 31271, 31277, 31307, 31319, 31321, 31327, 31333, 31337, 31357, 
            31379, 31387, 31391, 31393, 31397, 31469, 31477, 31481, 31489, 31511, 
            31513, 31517, 31531, 31541, 31543, 31547, 31567, 31573, 31583, 31601, 
            31607, 31627, 31643, 31649, 31657, 31663, 31667, 31687, 31699, 31721, 
            31723, 31727, 31729, 31741, 31751, 31769, 31771, 31793, 31799, 31817, 
            31847, 31849, 31859, 31873, 31883, 31891, 31907, 31957, 31963, 31973, 
            31981, 31991, 32003, 32009, 32027, 32029, 32051, 32057, 32059, 32063, 
            32069, 32077, 32083, 32089, 32099, 32117, 32119, 32141, 32143, 32159, 
            32173, 32183, 32189, 32191, 32203, 32213, 32233, 32237, 32251, 32257, 
            32261, 32297, 32299, 32303, 32309, 32321, 32323, 32327, 32341, 32353, 
            32359, 32363, 32369, 32371, 32377, 32381, 32401, 32411, 32413, 32423, 
            32429, 32441, 32443, 32467, 32479, 32491, 32497, 32503, 32507, 32531, 
            32533, 32537, 32561, 32563, 32569, 32573, 32579, 32587, 32603, 32609, 
            32611, 32621, 32633, 32647, 32653, 32687, 32693, 32707, 32713, 32717, 
            32719, 32749, 32771, 32779, 32783, 32789, 32797, 32801, 32803, 32831, 
            32833, 32839, 32843, 32869, 32887, 32909, 32911, 32917, 32933, 32939, 
            32941, 32957, 32969, 32971, 32983, 32987, 32993, 32999, 33013, 33023, 
            33029, 33037, 33049, 33053, 33071, 33073, 33083, 33091, 33107, 33113, 
            33119, 33149, 33151, 33161, 33179, 33181, 33191, 33199, 33203, 33211, 
            33223, 33247, 33287, 33289, 33301, 33311, 33317, 33329, 33331, 33343, 
            33347, 33349, 33353, 33359, 33377, 33391, 33403, 33409, 33413, 33427, 
            33457, 33461, 33469, 33479, 33487, 33493, 33503, 33521, 33529, 33533, 
            33547, 33563, 33569, 33577, 33581, 33587, 33589, 33599, 33601, 33613, 
            33617, 33619, 33623, 33629, 33637, 33641, 33647, 33679, 33703, 33713, 
            33721, 33739, 33749, 33751, 33757, 33767, 33769, 33773, 33791, 33797, 
            33809, 33811, 33827, 33829, 33851, 33857, 33863, 33871, 33889, 33893, 
            33911, 33923, 33931, 33937, 33941, 33961, 33967, 33997, 34019, 34031, 
            34033, 34039, 34057, 34061, 34123, 34127, 34129, 34141, 34147, 34157, 
            34159, 34171, 34183, 34211, 34213, 34217, 34231, 34253, 34259, 34261, 
            34267, 34273, 34283, 34297, 34301, 34303, 34313, 34319, 34327, 34337, 
            34351, 34361, 34367, 34369, 34381, 34403, 34421, 34429, 34439, 34457, 
            34469, 34471, 34483, 34487, 34499, 34501, 34511, 34513, 34519, 34537, 
            34543, 34549, 34583, 34589, 34591, 34603, 34607, 34613, 34631, 34649, 
            34651, 34667, 34673, 34679, 34687, 34693, 34703, 34721, 34729, 34739, 
            34747, 34757, 34759, 34763, 34781, 34807, 34819, 34841, 34843, 34847, 
            34849, 34871, 34877, 34883, 34897, 34913, 34919, 34939, 34949, 34961, 
            34963, 34981, 35023, 35027, 35051, 35053, 35059, 35069, 35081, 35083, 
            35089, 35099, 35107, 35111, 35117, 35129, 35141, 35149, 35153, 35159, 
            35171, 35201, 35221, 35227, 35251, 35257, 35267, 35279, 35281, 35291, 
            35311, 35317, 35323, 35327, 35339, 35353, 35363, 35381, 35393, 35401, 
            35407, 35419, 35423, 35437, 35447, 35449, 35461, 35491, 35507, 35509, 
            35521, 35527, 35531, 35533, 35537, 35543, 35569, 35573, 35591, 35593, 
            35597, 35603, 35617, 35671, 35677, 35729, 35731, 35747, 35753, 35759, 
            35771, 35797, 35801, 35803, 35809, 35831, 35837, 35839, 35851, 35863, 
            35869, 35879, 35897, 35899, 35911, 35923, 35933, 35951, 35963, 35969, 
            35977, 35983, 35993, 35999, 36007, 36011, 36013, 36017, 36037, 36061, 
            36067, 36073, 36083, 36097, 36107, 36109, 36131, 36137, 36151, 36161, 
            36187, 36191, 36209, 36217, 36229, 36241, 36251, 36263, 36269, 36277, 
            36293, 36299, 36307, 36313, 36319, 36341, 36343, 36353, 36373, 36383, 
            36389, 36433, 36451, 36457, 36467, 36469, 36473, 36479, 36493, 36497, 
            36523, 36527, 36529, 36541, 36551, 36559, 36563, 36571, 36583, 36587, 
            36599, 36607, 36629, 36637, 36643, 36653, 36671, 36677, 36683, 36691, 
            36697, 36709, 36713, 36721, 36739, 36749, 36761, 36767, 36779, 36781, 
            36787, 36791, 36793, 36809, 36821, 36833, 36847, 36857, 36871, 36877, 
            36887, 36899, 36901, 36913, 36919, 36923, 36929, 36931, 36943, 36947, 
            36973, 36979, 36997, 37003, 37013, 37019, 37021, 37039, 37049, 37057, 
            37061, 37087, 37097, 37117, 37123, 37139, 37159, 37171, 37181, 37189, 
            37199, 37201, 37217, 37223, 37243, 37253, 37273, 37277, 37307, 37309, 
            37313, 37321, 37337, 37339, 37357, 37361, 37363, 37369, 37379, 37397, 
            37409, 37423, 37441, 37447, 37463, 37483, 37489, 37493, 37501, 37507, 
            37511, 37517, 37529, 37537, 37547, 37549, 37561, 37567, 37571, 37573, 
            37579, 37589, 37591, 37607, 37619, 37633, 37643, 37649, 37657, 37663, 
            37691, 37693, 37699, 37717, 37747, 37781, 37783, 37799, 37811, 37813, 
            37831, 37847, 37853, 37861, 37871, 37879, 37889, 37897, 37907, 37951, 
            37957, 37963, 37967, 37987, 37991, 37993, 37997, 38011, 38039, 38047, 
            38053, 38069, 38083, 38113, 38119, 38149, 38153, 38167, 38177, 38183, 
            38189, 38197, 38201, 38219, 38231, 38237, 38239, 38261, 38273, 38281, 
            38287, 38299, 38303, 38317, 38321, 38327, 38329, 38333, 38351, 38371, 
            38377, 38393, 38431, 38447, 38449, 38453, 38459, 38461, 38501, 38543, 
            38557, 38561, 38567, 38569, 38593, 38603, 38609, 38611, 38629, 38639, 
            38651, 38653, 38669, 38671, 38677, 38693, 38699, 38707, 38711, 38713, 
            38723, 38729, 38737, 38747, 38749, 38767, 38783, 38791, 38803, 38821, 
            38833, 38839, 38851, 38861, 38867, 38873, 38891, 38903, 38917, 38921, 
            38923, 38933, 38953, 38959, 38971, 38977, 38993, 39019, 39023, 39041, 
            39043, 39047, 39079, 39089, 39097, 39103, 39107, 39113, 39119, 39133, 
            39139, 39157, 39161, 39163, 39181, 39191, 39199, 39209, 39217, 39227, 
            39229, 39233, 39239, 39241, 39251, 39293, 39301, 39313, 39317, 39323, 
            39341, 39343, 39359, 39367, 39371, 39373, 39383, 39397, 39409, 39419, 
            39439, 39443, 39451, 39461, 39499, 39503, 39509, 39511, 39521, 39541, 
            39551, 39563, 39569, 39581, 39607, 39619, 39623, 39631, 39659, 39667, 
            39671, 39679, 39703, 39709, 39719, 39727, 39733, 39749, 39761, 39769, 
            39779, 39791, 39799, 39821, 39827, 39829, 39839, 39841, 39847, 39857, 
            39863, 39869, 39877, 39883, 39887, 39901, 39929, 39937, 39953, 39971, 
            39979, 39983, 39989, 40009, 40013, 40031, 40037, 40039, 40063, 40087, 
            40093, 40099, 40111, 40123, 40127, 40129, 40151, 40153, 40163, 40169, 
            40177, 40189, 40193, 40213, 40231, 40237, 40241, 40253, 40277, 40283, 
            40289, 40343, 40351, 40357, 40361, 40387, 40423, 40427, 40429, 40433, 
            40459, 40471, 40483, 40487, 40493, 40499, 40507, 40519, 40529, 40531, 
            40543, 40559, 40577, 40583, 40591, 40597, 40609, 40627, 40637, 40639, 
            40693, 40697, 40699, 40709, 40739, 40751, 40759, 40763, 40771, 40787, 
            40801, 40813, 40819, 40823, 40829, 40841, 40847, 40849, 40853, 40867, 
            40879, 40883, 40897, 40903, 40927, 40933, 40939, 40949, 40961, 40973, 
            40993, 41011, 41017, 41023, 41039, 41047, 41051, 41057, 41077, 41081, 
            41113, 41117, 41131, 41141, 41143, 41149, 41161, 41177, 41179, 41183, 
            41189, 41201, 41203, 41213, 41221, 41227, 41231, 41233, 41243, 41257, 
            41263, 41269, 41281, 41299, 41333, 41341, 41351, 41357, 41381, 41387, 
            41389, 41399, 41411, 41413, 41443, 41453, 41467, 41479, 41491, 41507, 
            41513, 41519, 41521, 41539, 41543, 41549, 41579, 41593, 41597, 41603, 
            41609, 41611, 41617, 41621, 41627, 41641, 41647, 41651, 41659, 41669, 
            41681, 41687, 41719, 41729, 41737, 41759, 41761, 41771, 41777, 41801, 
            41809, 41813, 41843, 41849, 41851, 41863, 41879, 41887, 41893, 41897, 
            41903, 41911, 41927, 41941, 41947, 41953, 41957, 41959, 41969, 41981, 
            41983, 41999, 42013, 42017, 42019, 42023, 42043, 42061, 42071, 42073, 
            42083, 42089, 42101, 42131, 42139, 42157, 42169, 42179, 42181, 42187, 
            42193, 42197, 42209, 42221, 42223, 42227, 42239, 42257, 42281, 42283, 
            42293, 42299, 42307, 42323, 42331, 42337, 42349, 42359, 42373, 42379, 
            42391, 42397, 42403, 42407, 42409, 42433, 42437, 42443, 42451, 42457, 
            42461, 42463, 42467, 42473, 42487, 42491, 42499, 42509, 42533, 42557, 
            42569, 42571, 42577, 42589, 42611, 42641, 42643, 42649, 42667, 42677, 
            42683, 42689, 42697, 42701, 42703, 42709, 42719, 42727, 42737, 42743, 
            42751, 42767, 42773, 42787, 42793, 42797, 42821, 42829, 42839, 42841, 
            42853, 42859, 42863, 42899, 42901, 42923, 42929, 42937, 42943, 42953, 
            42961, 42967, 42979, 42989, 43003, 43013, 43019, 43037, 43049, 43051, 
            43063, 43067, 43093, 43103, 43117, 43133, 43151, 43159, 43177, 43189, 
            43201, 43207, 43223, 43237, 43261, 43271, 43283, 43291, 43313, 43319, 
            43321, 43331, 43391, 43397, 43399, 43403, 43411, 43427, 43441, 43451, 
            43457, 43481, 43487, 43499, 43517, 43541, 43543, 43573, 43577, 43579, 
            43591, 43597, 43607, 43609, 43613, 43627, 43633, 43649, 43651, 43661, 
            43669, 43691, 43711, 43717, 43721, 43753, 43759, 43777, 43781, 43783, 
            43787, 43789, 43793, 43801, 43853, 43867, 43889, 43891, 43913, 43933, 
            43943, 43951, 43961, 43963, 43969, 43973, 43987, 43991, 43997, 44017, 
            44021, 44027, 44029, 44041, 44053, 44059, 44071, 44087, 44089, 44101, 
            44111, 44119, 44123, 44129, 44131, 44159, 44171, 44179, 44189, 44201, 
            44203, 44207, 44221, 44249, 44257, 44263, 44267, 44269, 44273, 44279, 
            44281, 44293, 44351, 44357, 44371, 44381, 44383, 44389, 44417, 44449, 
            44453, 44483, 44491, 44497, 44501, 44507, 44519, 44531, 44533, 44537, 
            44543, 44549, 44563, 44579, 44587, 44617, 44621, 44623, 44633, 44641, 
            44647, 44651, 44657, 44683, 44687, 44699, 44701, 44711, 44729, 44741, 
            44753, 44771, 44773, 44777, 44789, 44797, 44809, 44819, 44839, 44843, 
            44851, 44867, 44879, 44887, 44893, 44909, 44917, 44927, 44939, 44953, 
            44959, 44963, 44971, 44983, 44987, 45007, 45013, 45053, 45061, 45077, 
            45083, 45119, 45121, 45127, 45131, 45137, 45139, 45161, 45179, 45181, 
            45191, 45197, 45233, 45247, 45259, 45263, 45281, 45289, 45293, 45307, 
            45317, 45319, 45329, 45337, 45341, 45343, 45361, 45377, 45389, 45403, 
            45413, 45427, 45433, 45439, 45481, 45491, 45497, 45503, 45523, 45533, 
            45541, 45553, 45557, 45569, 45587, 45589, 45599, 45613, 45631, 45641, 
            45659, 45667, 45673, 45677, 45691, 45697, 45707, 45737, 45751, 45757, 
            45763, 45767, 45779, 45817, 45821, 45823, 45827, 45833, 45841, 45853, 
            45863, 45869, 45887, 45893, 45943, 45949, 45953, 45959, 45971, 45979, 
            45989, 46021, 46027, 46049, 46051, 46061, 46073, 46091, 46093, 46099, 
            46103, 46133, 46141, 46147, 46153, 46171, 46181, 46183, 46187, 46199, 
            46219, 46229, 46237, 46261, 46271, 46273, 46279, 46301, 46307, 46309, 
            46327, 46337]


    def judgeSquareSum(self, c: int) -> bool:
        # Find prime factors of c.
        factors = []
        limit = int(math.sqrt(c)) + 1
        for p in self.primes:
            if p > limit or c == 1:
                break
            while c % p == 0:
                c //= p
                factors.append(p)
        if c != 1:
            factors.append(c)

        # Keep only those congruent to 3 mod 4    
        filtered_decomposition = Counter([f for f in factors if f % 4 == 3])

        # Return false if any such factor has an odd k
        for p, k in filtered_decomposition.items():
            if k % 2:
                return False

        # Otherwise, c can be written as a sum of two squares.
        return True
19800