This is simple version of harder [Square Sums](/kata/square-sums).

# Square sums

Write function `square_sums_row` (or `squareSumsRow`/`SquareSumsRow` depending on language rules) that, given integer number `N` (in range `2..43`), returns array of integers `1..N` arranged in a way, so sum of each 2 consecutive numbers is a square.

Solution is valid if and only if following two criterias are met:
1. Each number in range `1..N` is used once and only once.
2. Sum of each 2 consecutive numbers is a perfect square.

### Example
For N=15 solution could look like this:

`[ 9, 7, 2, 14, 11, 5, 4, 12, 13, 3, 6, 10, 15, 1, 8 ]`

### Verification

1. All numbers are used once and only once. When sorted in ascending order array looks like this:

`[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 ]`

2. Sum of each 2 consecutive numbers is a perfect square:

```
   16    16     16     16     16     16     16
   /+\   /+\    /+\    /+\    /+\    /+\    /+\
[ 9, 7, 2, 14, 11, 5, 4, 12, 13, 3, 6, 10, 15, 1, 8 ]
      \+/    \+/    \+/    \+/    \+/    \+/    \+/
       9     25      9     25      9     25      9

9 = 3*3
16 = 4*4
25 = 5*5
```

If there is no solution, return `false` (or, `None` in scala). For example if `N=5`, then numbers `1,2,3,4,5` cannot be put into square sums row: `1+3=4`, `4+5=9`, but
`2` has no pairs and cannot link `[1,3]` and `[4,5]`

# Have fun!

Harder version of this Kata is [here](/kata/square-sums).

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '# ==========================================================================================================================================\n# title         : squares, v2: faster with dictionnary instead of graph\n# description   :\n# author        : JR\n# date          : 28.04.20\n# version       :\n# IDE           : PyCharm\n# ==========================================================================================================================================\nimport math\n\n# code standard graphs (dirty-duct-copy networkx behavior)\nclass nx(dict):\n    @staticmethod\n    def empty_graph(nodes):\n        return nx(nodes)\n\n    @staticmethod\n    def squares_graph(n=23):\n        square_candidates = [(x+1)**2 for x in range(1, math.floor(math.sqrt(2*n-1)))]\n        G = nx.empty_graph(list(range(1, n+1)))\n\n        for s in square_candidates:\n            true_indexes = [x for x in range(1, 1+math.floor((s-1) / 2)) if s-x <= n]\n            for k in true_indexes:\n                G.add_edge(k, s-k)\n\n        return G\n\n    @staticmethod\n    def Graph(G):\n    # here we will implement the by-copy\n        return nx(G.copy())\n\n    def __init__(self, nodes, edges=None):\n        if edges is None:\n            if isinstance(nodes, dict):\n                # by-copy => this one should not really be used for our problem, but it is simpler at the beginning to be able to concentrate\n                # on the central matter\n                dict.__init__(self, {n: e.copy() for n,e in list(nodes.items())})\n            else:\n                dict.__init__(self, {n: set() for n in nodes})\n        else:\n            dict.__init__(self, {nodes[i]: edges[i] for i in range(len(nodes))})\n\n    def add_edge(self, x, y):\n        self[x] |= {y}\n        self[y] |= {x}\n\n    def remove_edge(self, x, y):\n        self[x] -= {y}\n        self[y] -= {x}\n\n    def remove_node(self, n):\n        edges = self[n].copy()\n        for e in edges:\n            self.remove_edge(n, e)\n\n        del self[n]\n\n    def display(self):\n        import matplotlib.pyplot as plt\n        import networkx as true_nx\n        plt.clf()\n        true_nx.draw(true_nx.Graph(G), labels={x: x for x in G.nodes})\n        plt.show()\n\n    @property\n    def nodes(self):\n        return list(self.keys())\n\n    @property\n    def degree(self):\n        return {(n, len(e)) for n, e in list(self.items())}\n\n\ndef square_sums_row(n):\n    return dfs_travel(n)\n\n\ndef dfs_travel(G=23, visit_ordered=None, N=None, display=False, verbose=False):\n    if isinstance(G, int):\n        G = nx.squares_graph(G)\n\n    if N is None:\n        N = len(G.nodes)\n\n    if visit_ordered is None:\n        visit_ordered = []\n\n    if len(visit_ordered) == N:\n        if verbose:\n            print(\'SUCCESS\')\n        return visit_ordered\n\n    impossible_nodes = [n for n, d in G.degree if d == 0]\n    if len(impossible_nodes) > 0:\n        return False\n    ending_nodes = [n for n, d in G.degree if d == 1]\n\n    if len(ending_nodes) > 2:\n        return False\n\n    if len(visit_ordered) == 0:\n\n        # We do the best guess to visit nodes by random... starting by most certain ones\n        if len(ending_nodes) > 0:\n            if verbose:\n                print(\'Guess zero\')\n            return dfs_travel(G, [ending_nodes[-1]], N, verbose=verbose)  # if two, it will arrive at the second node !\n\n        degrees = G.degree\n        max_degree = max([y for x, y in degrees])\n        for d in range(2, max_degree+1):\n            for n in [nd for nd, deg in degrees if deg == d]:\n                sol = dfs_travel(G, [n], verbose=verbose)\n                if sol != False:  # don\'t want the unsafe "if sol" with list\n                    if verbose:\n                        print(\'YESSS\')\n                    return sol\n\n        if verbose:\n            print(\'Exhausted guesses\')\n        return False\n\n    elif len(ending_nodes) == 2 and not visit_ordered[-1] in ending_nodes:\n        return False\n\n    G2 = nx.Graph(G)  # copy the graph... will need to improve if >100 graphs are needed !\n\n    last_idx = visit_ordered[-1]\n    for current_idx in G2[last_idx]: #.keys():\n        if verbose:\n            print((last_idx, current_idx))\n        visit_ordered.append(current_idx)\n        if verbose:\n            print(visit_ordered)\n        G3 = nx.Graph(G2)\n        G3.remove_node(last_idx)\n        sol = dfs_travel(G3, visit_ordered, N, verbose=verbose)\n\n        if sol != False:\n            return visit_ordered\n\n        visit_ordered.pop()\n    if verbose:\n        print(visit_ordered)\n        print((len(visit_ordered) - N))\n    return False\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'square_sums_row'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 11404