import json
import collections
import functools

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974]}, {"Source": "4", "ID": "14", "Date": "2021-02-01", "Weight": "1398", "Edges": [940, 941, 965, 969, 978, 993]}, {"Source": "11", "ID": "5", "Date": "2021-02-02", "Weight": "1227", "Edges": [957, 964, 989, 994]}, {"Source": "3", "ID": "12", "Date": "2021-02-03", "Weight": "130", "Edges": [942, 954, 966, 997]}, {"Source": "7", "ID": "8", "Date": "2021-02-04", "Weight": "705", "Edges": [934, 950, 951, 976, 980]}, {"Source": "9", "ID": "15", "Date": "2021-02-05", "Weight": "1884", "Edges": [933, 974]}, {"Source": "11", "ID": "5", "Date": "2021-02-06", "Weight": "1425", "Edges": [957, 964, 989, 994]}, {"Source": "11", "ID": "16", "Date": "2021-02-07", "Weight": "234", "Edges": [937, 946, 967, 979, 983, 995]}, {"Source": "6", "ID": "10", "Date": "2021-02-08", "Weight": "1618", "Edges": [958, 959, 987]}, {"Source": "20", "ID": "20", "Date": "2021-02-09", "Weight": "176", "Edges": [952, 990]}, {"Source": "6", "ID": "17", "Date": "2021-02-10", "Weight": "1803", "Edges": [938, 943, 968, 977]}, {"Source": "15", "ID": "15", "Date": "2021-02-11", "Weight": "520", "Edges": [974]}, {"Source": "8", "ID": "7", "Date": "2021-02-12", "Weight": "307", "Edges": [960]}, {"Source": "6", "ID": "3", "Date": "2021-02-13", "Weight": "910", "Edges": [973, 998]}, {"Source": "18", "ID": "15", "Date": "2021-02-14", "Weight": "1589", "Edges": [974]}, {"Source": "16", "ID": "6", "Date": "2021-02-15", "Weight": "1982", "Edges": [948, 949, 962, 986]}, {"Source": "17", "ID": "12", "Date": "2021-02-16", "Weight": "1849", "Edges": [942, 954, 966, 997]}, {"Source": "9", "ID": "20", "Date": "2021-02-17", "Weight": "1484", "Edges": [952, 990]}, {"Source": "14", "ID": "10", "Date": "2021-02-18", "Weight": "228", "Edges": [958, 959, 987]}, {"Source": "14", "ID": "11", "Date": "2021-02-19", "Weight": "1195", "Edges": [963, 981, 982]}, {"Source": "12", "ID": "1", "Date": "2021-02-20", "Weight": "654", "Edges": []}, {"Source": "17", "ID": "3", "Date": "2021-02-21", "Weight": "697", "Edges": [973, 998]}, {"Source": "19", "ID": "11", "Date": "2021-02-22", "Weight": "1375", "Edges": [963, 981, 982]}, {"Source": "1", "ID": "13", "Date": "2021-02-23", "Weight": "1449", "Edges": [972]}, {"Source": "16", "ID": "18", "Date": "2021-02-24", "Weight": "935", "Edges": [971, 985]}, {"Source": "1", "ID": "14", "Date": "2021-02-25", "Weight": "1506", "Edges": [965, 969, 978, 993]}, {"Source": "6", "ID": "1", "Date": "2021-02-26", "Weight": "874", "Edges": []}, {"Source": "6", "ID": "5", "Date": "2021-02-27", "Weight": "116", "Edges": [957, 964, 989, 994]}, {"Source": "8", "ID": "19", "Date": "2021-02-28", "Weight": "601", "Edges": [991, 999]}, {"Source": "8", "ID": "9", "Date": "2021-03-01", "Weight": "676", "Edges": [955, 956, 961, 992]}, {"Source": "20", "ID": "15", "Date": "2021-03-02", "Weight": "496", "Edges": [974]}, {"Source": "4", "ID": "18", "Date": "2021-03-03", "Weight": "580", "Edges": [971, 985]}, {"Source": "12", "ID": "4", "Date": "2021-03-04", "Weight": "484", "Edges": []}, {"Source": "9", "ID": "1", "Date": "2021-03-05", "Weight": "618", "Edges": []}, {"Source": "9", "ID": "8", "Date": "2021-03-06", "Weight": "883", "Edges": [976, 980]}, {"Source": "5", "ID": "17", "Date": "2021-03-07", "Weight": "1072", "Edges": [968, 977]}, {"Source": "10", "ID": "16", "Date": "2021-03-08", "Weight": "591", "Edges": [967, 979, 983, 995]}, {"Source": "10", "ID": "19", "Date": "2021-03-09", "Weight": "1793", "Edges": [991, 999]}, {"Source": "7", "ID": "4", "Date": "2021-03-10", "Weight": "726", "Edges": []}, {"Source": "9", "ID": "10", "Date": "2021-03-11", "Weight": "1378", "Edges": [987]}, {"Source": "6", "ID": "3", "Date": "2021-03-12", "Weight": "1337", "Edges": [973, 998]}, {"Source": "11", "ID": "8", "Date": "2021-03-13", "Weight": "161", "Edges": [976, 980]}, {"Source": "5", "ID": "3", "Date": "2021-03-14", "Weight": "1775", "Edges": [973, 998]}, {"Source": "14", "ID": "18", "Date": "2021-03-15", "Weight": "323", "Edges": [971, 985]}, {"Source": "12", "ID": "16", "Date": "2021-03-16", "Weight": "675", "Edges": [967, 979, 983, 995]}, {"Source": "16", "ID": "4", "Date": "2021-03-17", "Weight": "1729", "Edges": []}, {"Source": "17", "ID": "8", "Date": "2021-03-18", "Weight": "1651", "Edges": [976, 980]}, {"Source": "14", "ID": "11", "Date": "2021-03-19", "Weight": "1764", "Edges": [981, 982]}, {"Source": "1", "ID": "9", "Date": "2021-03-20", "Weight": "1228", "Edges": [992]}, {"Source": "18", "ID": "5", "Date": "2021-03-21", "Weight": "1257", "Edges": [989, 994]}, {"Source": "13", "ID": "13", "Date": "2021-03-22", "Weight": "1710", "Edges": []}, {"Source": "3", "ID": "20", "Date": "2021-03-23", "Weight": "1009", "Edges": [990]}, {"Source": "15", "ID": "15", "Date": "2021-03-24", "Weight": "958", "Edges": []}, {"Source": "1", "ID": "17", "Date": "2021-03-25", "Weight": "1317", "Edges": [977]}, {"Source": "8", "ID": "9", "Date": "2021-03-26", "Weight": "1937", "Edges": [992]}, {"Source": "17", "ID": "14", "Date": "2021-03-27", "Weight": "1015", "Edges": [978, 993]}, {"Source": "14", "ID": "20", "Date": "2021-03-28", "Weight": "260", "Edges": [990]}, {"Source": "16", "ID": "2", "Date": "2021-03-29", "Weight": "1721", "Edges": [984, 996]}, {"Source": "8", "ID": "13", "Date": "2021-03-30", "Weight": "1221", "Edges": []}, {"Source": "11", "ID": "17", "Date": "2021-03-31", "Weight": "724", "Edges": []}, {"Source": "11", "ID": "4", "Date": "2021-04-01", "Weight": "232", "Edges": []}, {"Source": "16", "ID": "7", "Date": "2021-04-02", "Weight": "107", "Edges": []}, {"Source": "2", "ID": "8", "Date": "2021-04-03", "Weight": "1023", "Edges": []}, {"Source": "18", "ID": "14", "Date": "2021-04-04", "Weight": "469", "Edges": [993]}, {"Source": "6", "ID": "10", "Date": "2021-04-05", "Weight": "1179", "Edges": [987]}, {"Source": "10", "ID": "9", "Date": "2021-04-06", "Weight": "1816", "Edges": [992]}, {"Source": "1", "ID": "12", "Date": "2021-04-07", "Weight": "783", "Edges": [997]}, {"Source": "5", "ID": "13", "Date": "2021-04-08", "Weight": "696", "Edges": []}, {"Source": "20", "ID": "11", "Date": "2021-04-09", "Weight": "767", "Edges": []}, {"Source": "19", "ID": "12", "Date": "2021-04-10", "Weight": "1164", "Edges": [997]}, {"Source": "9", "ID": "12", "Date": "2021-04-11", "Weight": "254", "Edges": [997]}, {"Source": "14", "ID": "15", "Date": "2021-04-12", "Weight": "533", "Edges": []}, {"Source": "5", "ID": "4", "Date": "2021-04-13", "Weight": "1740", "Edges": []}, {"Source": "16", "ID": "5", "Date": "2021-04-14", "Weight": "1771", "Edges": []}, {"Source": "2", "ID": "8", "Date": "2021-04-15", "Weight": "1353", "Edges": []}, {"Source": "12", "ID": "8", "Date": "2021-04-16", "Weight": "347", "Edges": []}, {"Source": "3", "ID": "12", "Date": "2021-04-17", "Weight": "1678", "Edges": []}, {"Source": "19", "ID": "8", "Date": "2021-04-18", "Weight": "1904", "Edges": []}]'''

data = json.loads(data)

class Path:
    #Construct the trip with initial values
    def __init__(self, weight, vertices):
        self.weight = weight
        self.vertices = vertices

@functools.lru_cache(maxsize=None)
def recursiveTraversal(originIndex, target, steps):
    startingVertex = data[originIndex]

    if startingVertex["ID"] == target:
        if steps == 0:
            return Path(0, [])
        else:
            return None
    else:
        if steps == 0:
            return None
        else:
            potentialPaths = []
            for i in startingVertex["Edges"]:
                nextVertex = data[i]
                nextPath = recursiveTraversal(i, target, steps - 1)
                if nextPath == None:
                    continue
                nextPath.weight += int(nextVertex["Weight"])
                nextPath.vertices.append(i)

                potentialPaths.append(nextPath)
            if len(potentialPaths) > 0:
                minPath = min(potentialPaths, key=lambda x: x.weight)
                return minPath
            else:
                return None


print(recursiveTraversal(0, "1", 3).vertices)