I'd like to create a Python program that can help me figure out how many different ways an integer can be represented as a sum of primes. So, the program would accept a positive integer as an argument, and then output the number of ways that primes could be added together to make the integer. However, I'd like to discard any duplicate cases. For example, the number 7 could be represented by the following set of five sums of primes:

2+2+3
2+3+2
5+2
2+5
3+2+2

But this seems redundant. I'd like to remove all of the reordered cases from the output. So the number 7 would only have two valid sums

2+2+3
2+5

I'd like the program to have at least two functions, but as many as necessary. I want to have an I/O function that accepts a validated integer input and provides the output and then asks the user if they'd like to submit another integer with a yes/no input, which should also be validated. I'd like the program to be written without the use of any special libraries or library functions.
system
main ek paythan kaarykram bananaa chahta hum jo mujhe yah pataa lagane main madad kar sake ki ek purnank ko prime ke yoga ke rup main kitne alag -alag tareekon se darshaya ja saktaa he.to, kaarykram ek sakaaratmak purnank ko ek tark ke rup main sweekaar karegaa, or phir un tareekon kii sankhya kaa utpaadan karegaa jo purnank banane ke liye ek saath jode ja sakate hai.haalaanki, main kisi bhi dupliket maamalon ko chhodana chahta hum.udhaaharan ke liye, sankhya 7 ko paanch rakamon ke nimnlikhit set dwaara darshaya ja saktaa he:

2+2+3
2+3+2
5+2
2+5
3+2+2

lekin yah bemaani lagata he.main output se sabhi reordered maamalon ko hataanaa chahta hum.isliye number 7 main keval do vaid rakamen hongi

2+2+3
2+5

main chaahunga ki kaarykram kam se kam do kaary karen, lekin jitne aavashyak ho.main ek I/O fnction rakhana chahta hum jo ek maanya purnank input ko sweekaar karata he or output pradaan karata he or phir upyogkarta se poochta he ki kya ve ek or purnank ko YES/NO input ke saath sabamit karnaa chaahate hai, jise maanya bhi kiya janaa chahie.main kisi vishesh pustkaalay yaa pustkaalay kaaryon ke upyog ke bina likhaa janaa chahta hum.
user
yahaan aapke anurodh ko sambodhit karne kaa ek tarika he.yah kaarykram madhyavarti parinaamon ko sangrahit karke or unhen pun: upyog karke pradarshan main sudhaar karne ke liye pramukh sankhyaon kii ek talika ke sansmaran kaa upyog karata he.kaarykram anurodh karata he ki upyogkarta ek sakaaratmak purnank input pradaan karata he or yah sunishchit karne ke liye input ko maanya karata he ki upyogkarta ne ek sakaaratmak purnank pradaan kiya he.kaarykram tab moolyankan karata he ki kya input teen vishesh maamalon main se ek he, maan 1, 2, yaa 3, kyonki in maanon ko prime numberon ke yoga dwaara darshaya nahin ja saktaa he.yadi input mukhya fnction main paribhaashit vishesh maamalon ke bheetar nahin aata he, to input ko counting fnction ke liye ek tark ke rup main paarit kiya jaataa he, jo un tareekon kii sankhya kii gananaa karata he jo purnank ko pramukh sankhyaon ke yoga ke rup main darshaya ja saktaa he.kaarykram tab is maan ko lautaata he or phir upyogkarta se poochta he ki kya ve moolyankan ke liye ek or purnank prastut karnaa chaahate hai.

def is_prime (n):
    yadi n <= 1:
        vivaran jhootha he
    main range main (2, int (n ** 0.5) + 1) ke liye:
        yadi n % i == 0:
            vivaran jhootha he
    sahi vaapasi

def count_sum_of_primes (n):
    prime_memory = {}

    def count_funct (n, primes):
        yadi n == 0:
            lauten 1
        yadi n <0:
            vaapasi 0
        if (n, tuple (primes)) prime_memory main:
            Prime_Memory [(n, tuple (primes))]]
        ginati = 0
        ke liye main range (len (primes)) main:
            ginati += count_funct (n - primes [i], primes [i:])
        prime_memory [(n, tuple (primes))] = ginati
        vaapasi gananaa

    primes = [i ke liye i in range (2, n) agar is_prime (i)]
    COUNT_FUNCT (n, primes) lauten

def input_positive_integer (sheeghra):
    jabaki sach:
        koshish karnaa:
            sankhya = int (input (sheeghra))
            yadi sankhya> 0:
                vaapasi sankhya
            anya:
                print ("kripaya ek sakaaratmak purnank darj karen.")
        ValueError ko chhodkar:
            print ("amaanya input. kripaya ek maanya purnank darj karen.")

def main ():
    jabaki sach:
        n = input_positive_integer ("ek sakaaratmak purnank darj karen:")
        
        yadi n == 1 yaa n == 2 yaa n == 3:
            yadi is_prime (n):
                print (f "{n} ek pramukh sankhya he, lekin do yaa adhik primes ke yoga ke rup main pratinidhitiv nahin kiya ja saktaa he.")
            anya:
                print (f "{n} ek pramukh sankhya nahin he or ise primes ke yoga ke rup main darshaya nahin ja saktaa he.")
        anya:
            count = count_sum_of_primes (n)
            print (f "tareekon kii sankhya {n} ko primes ke yoga ke rup main darshaya ja saktaa he {ginati}.")
        
        jabaki sach:
            input_loop = Input ("kya aap moolyankan ke liye ek or purnank prastut karnaa chahenge? (haan/nahin):") .lower (). strip ()
            yadi input_loop ['haan', 'y'] main:
                todna
            ELIF INPUT_LOOP ['nahin', 'n'] main:
                print ("alavida.")
                waapas karnaa
            anya:
                print ("amaanya input. kripaya haa yaa number darj karen")

yadi __name__ == "__main__":
    mukhya()
assistant
<|system|>
</s>
<|user|>
main ek paythan kaarykram bananaa chahta hum jo mujhe yah pataa lagane main madad kar sake ki ek purnank ko prime ke yoga ke rup main kitne alag -alag tareekon se darshaya ja saktaa he.to, kaarykram ek sakaaratmak purnank ko ek tark ke rup main sweekaar karegaa, or phir un tareekon kii sankhya kaa utpaadan karegaa jo purnank banane ke liye ek saath jode ja sakate hai.haalaanki, main kisi bhi dupliket maamalon ko chhodana chahta hum.udhaaharan ke liye, sankhya 7 ko paanch rakamon ke nimnlikhit set dwaara darshaya ja saktaa he:

2+2+3
2+3+2
5+2
2+5
3+2+2

lekin yah bemaani lagata he.main output se sabhi reordered maamalon ko hataanaa chahta hum.isliye number 7 main keval do vaid rakamen hongi

2+2+3
2+5

main chaahunga ki kaarykram kam se kam do kaary karen, lekin jitne aavashyak ho.main ek I/O fnction rakhana chahta hum jo ek maanya purnank input ko sweekaar karata he or output pradaan karata he or phir upyogkarta se poochta he ki kya ve ek or purnank ko YES/NO input ke saath sabamit karnaa chaahate hai, jise maanya bhi kiya janaa chahie.main kisi vishesh pustkaalay yaa pustkaalay kaaryon ke upyog ke bina likhaa janaa chahta hum.</s>
<|assistant|>
yahaan aapke anurodh ko sambodhit karne kaa ek tarika he.yah kaarykram madhyavarti parinaamon ko sangrahit karke or unhen pun: upyog karke pradarshan main sudhaar karne ke liye pramukh sankhyaon kii ek talika ke sansmaran kaa upyog karata he.kaarykram anurodh karata he ki upyogkarta ek sakaaratmak purnank input pradaan karata he or yah sunishchit karne ke liye input ko maanya karata he ki upyogkarta ne ek sakaaratmak purnank pradaan kiya he.kaarykram tab moolyankan karata he ki kya input teen vishesh maamalon main se ek he, maan 1, 2, yaa 3, kyonki in maanon ko prime numberon ke yoga dwaara darshaya nahin ja saktaa he.yadi input mukhya fnction main paribhaashit vishesh maamalon ke bheetar nahin aata he, to input ko counting fnction ke liye ek tark ke rup main paarit kiya jaataa he, jo un tareekon kii sankhya kii gananaa karata he jo purnank ko pramukh sankhyaon ke yoga ke rup main darshaya ja saktaa he.kaarykram tab is maan ko lautaata he or phir upyogkarta se poochta he ki kya ve moolyankan ke liye ek or purnank prastut karnaa chaahate hai.

def is_prime (n):
    yadi n <= 1:
        vivaran jhootha he
    main range main (2, int (n ** 0.5) + 1) ke liye:
        yadi n % i == 0:
            vivaran jhootha he
    sahi vaapasi

def count_sum_of_primes (n):
    prime_memory = {}

    def count_funct (n, primes):
        yadi n == 0:
            lauten 1
        yadi n <0:
            vaapasi 0
        if (n, tuple (primes)) prime_memory main:
            Prime_Memory [(n, tuple (primes))]]
        ginati = 0
        ke liye main range (len (primes)) main:
            ginati += count_funct (n - primes [i], primes [i:])
        prime_memory [(n, tuple (primes))] = ginati
        vaapasi gananaa

    primes = [i ke liye i in range (2, n) agar is_prime (i)]
    COUNT_FUNCT (n, primes) lauten

def input_positive_integer (sheeghra):
    jabaki sach:
        koshish karnaa:
            sankhya = int (input (sheeghra))
            yadi sankhya> 0:
                vaapasi sankhya
            anya:
                print ("kripaya ek sakaaratmak purnank darj karen.")
        ValueError ko chhodkar:
            print ("amaanya input. kripaya ek maanya purnank darj karen.")

def main ():
    jabaki sach:
        n = input_positive_integer ("ek sakaaratmak purnank darj karen:")
        
        yadi n == 1 yaa n == 2 yaa n == 3:
            yadi is_prime (n):
                print (f "{n} ek pramukh sankhya he, lekin do yaa adhik primes ke yoga ke rup main pratinidhitiv nahin kiya ja saktaa he.")
            anya:
                print (f "{n} ek pramukh sankhya nahin he or ise primes ke yoga ke rup main darshaya nahin ja saktaa he.")
        anya:
            count = count_sum_of_primes (n)
            print (f "tareekon kii sankhya {n} ko primes ke yoga ke rup main darshaya ja saktaa he {ginati}.")
        
        jabaki sach:
            input_loop = Input ("kya aap moolyankan ke liye ek or purnank prastut karnaa chahenge? (haan/nahin):") .lower (). strip ()
            yadi input_loop ['haan', 'y'] main:
                todna
            ELIF INPUT_LOOP ['nahin', 'n'] main:
                print ("alavida.")
                waapas karnaa
            anya:
                print ("amaanya input. kripaya haa yaa number darj karen")

yadi __name__ == "__main__":
    mukhya()</s>
