This is what we're given:
```
from Crypto.Util.number import getPrime

p = getPrime(1024)
q = getPrime(1024)
N = p * q
e = 0x10001

with open('flag.txt', 'rb') as f:
flag = f.read()

assert len(flag) == 33

flag_header = flag[:7] # TSGCTF{
flag_content = flag[7:-1]
flag_footer = flag[-1:] # }

assert len(flag_content) == len({byte for byte in flag_content}) # flag_content is unique

c_list = [pow(byte, e, N) for byte in flag]
clues = [x * y % N for x, y in zip(c_list[:-1], c_list[1:])]
clues.sort()

print(f'N = {N}')
print(f'e = {e}')
print(f'clues = {clues}')
```

We're given N, e, and the clues in output.txt. I've included them in my solution code down below.

Seems like we have no unique characters.
We're also given the multiplication of the RSA encryptions of each pair of consecutive bytes, albeit in some shuffled order.

Here's the idea behind the solution:
Because we're given the multiplication of the RSA encryptions of consecutive bytes, we can essentially brute force combinations of possible characters for each clue.
The only problem is there may be collisions, i.e. the same two characters produce the same clue value.
To get around this, we can employ both the fact that we have only unique characters and a little bit of common sense to figure out the flag!

The implementation is simple.

1. Create a list of possible characters
2. Iterate through all clues
3. Iterate through all pairs of possible characters with two nested for loops
4. Check if they are a valid pair for the flag.
5. If they are, add them to an adjacency map that essentially stores a list of all characters that can be next to the key.
5.5 Make sure to add it by using both orders of a (key, value) pair
6. Once the iterating is all done, remove all the consecutive characters of the flag prefix to make it easier to figure out
7. With the final adjacency list, use unique characters and some common sense to get the flag!
7.5 You could technically implement BFS to find a path from the '{' to the '}' for a more rigorous solution, but I was too lazy to do that
8. Profit!

Here's the adjacency map:

{'s': ['I', 'T'], 'I': ['s', ','], 'f': ['l', '-'], 'l': ['f', 'F', '8', 'a'], 'C': [], 'G': [], 'd': ['!', 'U'], '!': ['d'], 'B': ['2', 'T'], '2': ['B'], 'K': [',', 'O'], ',': ['K', 'I', '~'], '7': ['<', 'b'], '<': ['7', '~', 'b'], 'n': ['u', '1'], 'u': ['n', '_'], 'e': ['U', '-'], 'U': ['e', '6', 'd', 'q'], 'S': [], 'T': ['s', 'Z', 'H', 'B'], '-': ['f', 'e'], '6': ['U', 'p'], 'Z': ['3', 'T'], '3': ['Z'], 'A': ['5', '_'], '5': ['A', 'i'], 'O': ['K', '{'], 'g': ['?', 'a'], '?': ['g', 'x', '`', 'X'], 'D': ['X', '}'], 'X': ['D', '?'], 'i': ['5', '\\', 'H', 'R', '8'], '\\': ['i'], 'q': ['1', 'U'], '1': ['q', 'x', 'n'], 'H': ['i', 'T', 'M'], 'F': ['l', 'M'], 'x': ['?', '1'], '~': ['<', '0', ','], 'R': ['i'], '{': ['O'], 'b': ['<', '7'], '8': ['i', 'l', 'c'], 'p': ['6'], '0': ['~'], '`': ['?'], '}': ['D'], '_': ['A', 'u'], 'a': ['g', 'l'], 'M': ['F', 'H'], 'c': ['8']}

And here is our flag!

TSGCTF{OK,IsTHi5A_un1qUe-flag?XD}

The actual implementation follows below:

```
N = 23270433480920204754247611545325351123344837487480637119344134402239723224072753511766733288907047277110318616688410345451695008290697208699431350412549980332693080979894504737640802849242656337537061128034361792156302502329044951868719492095983428863678764573927362740207756141512536958600798465368672826288270218390845725069636496528488276905161318078890887808033722334376853632300178257589009018165644740844747444214979597702959381078126401914809713991087656801656368079319383579542103855944156160231935875884314630699684359910296730669798237991501134339113682532446997472722560474195749179320370386661938616345489
e = 65537
clues = [790128007826920672966041424911766354167695121053219604283198146207007061791691778597663178563455647947105718896263099495348666331968821896627253287975936857535926164644548223394731131868459847861503995994130787209417795249554290922334587840664276128893082715626698208421033163870050616673531495044580102830036983208043090136212931697438690030675611301000171270559392107484305007589373493054650247495594665847524590737367285135216109196557363472975056201832374767680569696302197844301099024043070258479146726214414688459938129079248125143388403636784068208501745074616490491553776387248926153964494371491351883633209, 2603711767185838325352475153597847161854130118046369285623915043550612314176250745686994158628404520769025735077328213489305045750703593138538988340789187229888984902266067604215108157628606721779126603704209046389682027226116051092595210765409544706918465385789940134172311788347486915924020739666375005469879097995622537311532236494537245411805276338873499191960938465585934543775755531517716535416304391622644348521922876999587501073379321712481689748053619310595304248483018790236975241904276396525088600521271478581198340688684196813199138458166434400373640927130152301112142288723416868406008752554068971897796, 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from string import punctuation

possiblechars = []
for i in range(26):
possiblechars.append(chr(ord('a') + i))
for i in range(26):
possiblechars.append(chr(ord('A') + i))
for i in range(10):
possiblechars.append(str(i))

'''
possiblechars.append('_')
possiblechars.append('!')
possiblechars.append('?')
'''
for i in punctuation:
possiblechars.append(i)

adj = dict()
for i in range(len(clues)):
print(i)
for j in range(len(possiblechars)):
jchar = possiblechars[j]
for k in range(j, len(possiblechars)):
kchar = possiblechars[k]
c1 = pow(ord(jchar), e, N)
c2 = pow(ord(kchar), e, N)
if c1 * c2 % N == clues[i]:
if jchar not in adj:
adj[jchar] = []
if kchar not in adj:
adj[kchar] = []
adj[jchar].append(kchar)
adj[kchar].append(jchar)
print(jchar, kchar)

m = 'TSGCTF{'
for i in range(len(m)):
if i > 0:
adj[m[i]].remove(m[i - 1])
if i < len(m) - 1:
adj[m[i]].remove(m[i + 1])

print(adj)
```