qyliang/CodeNanoFix huggingface dataset:
Buggy code:
N = int(input())
a = []
count =0
count2 = 0
count3 = 0
print(N)
X=int(N**0.5)
for i in range(X+1):
	if i ==0 or i == 1:
		pass
	elif N % i == 0:

		while N % i==0:
			N /= i
			count2 += 1
		j =1
		count3 = 0
		while count2 - j >=0:
			count2 -= j
			j = j+1
			count3 += 1 
		count += count3 		
		count2 = 0            
if count ==0 and N >1:
	count =1
print(count)

Fixed code:
N = int(input())
a = []
count =0
count2 = 0
count3 = 0
X=int(N**0.5)
for i in range(X+1):
	if i ==0 or i == 1:
		pass
	elif N % i == 0:

		while N % i==0:
			N /= i
			count2 += 1
		j =1
		count3 = 0
		while count2 - j >=0:
			count2 -= j
			j = j+1
			count3 += 1 
		count += count3 		
		count2 = 0            
if  N >1:
	count +=1
print(count)
Buggy code:
#!/usr/bin/env python3

import sys
import math
from bisect import bisect_right as br
from bisect import bisect_left as bl
sys.setrecursionlimit(2147483647)
from heapq import heappush, heappop,heappushpop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))

n = I()
ans = 0
m = n
for i in range(2, int(math.sqrt(n)) + 1):
    if n % i == 0:
        cnt = 0
        while n % i == 0:
            cnt += 1
            n //= i
        tmp = 1
        while cnt >= tmp:
            ans += 1
            cnt -= tmp
            tmp += 1
if n % m == 0:
    ans += 1
print(ans)

Fixed code:
#!/usr/bin/env python3

import sys
import math
from bisect import bisect_right as br
from bisect import bisect_left as bl
sys.setrecursionlimit(2147483647)
from heapq import heappush, heappop,heappushpop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))

n = I()
ans = 0
for i in range(2, int(math.sqrt(n)) + 1):
    if n % i == 0:
        cnt = 0
        while n % i == 0:
            cnt += 1
            n //= i
        tmp = 1
        while cnt >= tmp:
            ans += 1
            cnt -= tmp
            tmp += 1
if n != 1:
    ans += 1
print(ans)
Buggy code:
import math

n = int(input())
d = n
m = {}

for i in range(2, int(math.sqrt(n)) + 1):
    m[i] = 0
    while (d % i == 0):
        d //= i
        m[i]+=1
res = 0
print(m)
for i in m.values():
    res+=int(math.sqrt(i*2))
if d > 1:
    res += 1
print(res)


Fixed code:
import math

n = int(input())
d = n
m = {}

for i in range(2, int(math.sqrt(n)) + 1):
    m[i] = 0
    while (d % i == 0):
        d //= i
        m[i]+=1
res = 0
for i in m.values():
    res+=int(math.sqrt(i*2+0.25)-0.5)

if d > 1:
    res += 1
print(res)
Buggy code:
n=int(input())
d={}
for k in range(2, 10**6):
  while n%k<1: n//k; d[k]=d.get(k, 0)+1
a=0
for i in d.values():
  t=c=0
  while t+c<i: c+=1; t+=c
  a+=c
print(a+(n>1))


Fixed code:
n=int(input())
d={}
for k in range(2,10**6):
  while n%k<1: n//=k; d[k]=d.get(k,0)+1
a=0
for i in d.values():
  t=c=0
  while t+c<i: c+=1; t+=c
  a+=c
print(a+(n>1))
Buggy code:
import numpy as np
import sys
A=a=int(input())
count=2
samenumcount=0
y=[]
 
if A==1:
    print(0)
    sys.exit()
 
while A!=1 and count<np.sqrt(a):
    if A%count==0:
        samenumcount+=1
        y.append(count**samenumcount)
        A=A/count
    else:
        count+=1
        samenumcount=0
y.sort()
 
count2=0
for i in y:
    if a==1:
      break
    if a%i==0:
        a=a/i
        count2+=1
 
if count2==0 or a!=1:
    count2+=1

print(count2)

Fixed code:
import numpy as np
import sys
A=a=int(input())
count=2
samenumcount=0
y=[]
 
if A==1:
    print(0)
    sys.exit()
 
while A!=1 and count<np.sqrt(a):
    if A%count==0:
        samenumcount+=1
        y.append(count**samenumcount)
        A=A/count
    else:
        count+=1
        samenumcount=0
if A!=1:
    y.append(A)
y.sort()
count2=0
for i in y:
    if a==1:
      break
    if a%i==0:
        a=a/i
        count2+=1
 
if count2==0:
    count2+=1

print(count2)
Buggy code:

def factorization(n):
  arr = []
  temp = n
  for i in range(2, int(-(-n**0.5//1))+1):
    if temp%i==0:
      cnt=0
      while temp%i==0:
        cnt+=1
        temp //= i
      arr.append([i, cnt])

  if temp!=1:
    arr.append([temp, 1])

  if arr==[]:
    arr.append([n, 1])

  return arr

def main():
  n = int(input())
  lst = factorization(n)

  ans = 0
  for _a, b in lst:
    i = 1
    while i <= b:
      b -= i
      i += 1
      ans += 1

  print(ans)

main()


Fixed code:

def factorization(n):
  arr = []
  temp = n
  for i in range(2, int(-(-n**0.5//1))+1):
    if temp%i==0:
      cnt=0
      while temp%i==0:
        cnt+=1
        temp //= i
      arr.append([i, cnt])

  if temp!=1:
    arr.append([temp, 1])

  if arr==[]:
    arr.append([n, 1])

  return arr

def main():
  n = int(input())
  lst = factorization(n)

  ans = 0
  for a, b in lst:
    if a == 1:
      continue

    i = 1
    while i <= b:
      b -= i
      i += 1
      ans += 1

  print(ans)

main()
Buggy code:
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])
    if temp!=1:
        arr.append([temp, 1])
    if arr==[]:
        arr.append([n, 1])
    return arr
N = int(input())
a = factorization(N)
cnt = 0
for i in a:
  temp = i[1]-1
  d = 2
  while temp>=d:
    temp -= d
    d += 1
  cnt+=d-1
print(cnt)
  
  
  
  
  
  

Fixed code:
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])
    if temp!=1:
        arr.append([temp, 1])
    if arr==[]:
        arr.append([n, 1])
    return arr
N = int(input())
if N == 1:
  print(0)
  exit()
a = factorization(N)
cnt = 0
for i in a:
  temp = i[1]-1
  d = 2
  while temp>=d:
    temp -= d
    d += 1
  cnt+=d-1
print(cnt)
Buggy code:
#!/usr/bin/env python3
import sys

from functools import reduce

import math


from collections import defaultdict
from math import sqrt

def prime_factors(n):
    primes = defaultdict(int)
    i = 2
    while n != 1:
        if n % i == 0:
            n = n // i
            primes[i] += 1
        if i > sqrt(n) and len(primes)==0:
            primes[i] += 1
            break
        else:
            i += 1
    return primes

def solve_n(x):
    return (-1 + sqrt(1 + 4 * 2* x)) / 2

def solve(N: int):
    fs = prime_factors(N)
    count = 0
    for key, value in fs.items():
        count += math.floor(solve_n(value))

    print(count)
    return



# Generated by 1.1.7.1 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word

    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    solve(N)


if __name__ == "__main__":
    main()


Fixed code:
#!/usr/bin/env python3
import sys

from functools import reduce

import math


from collections import defaultdict
from math import sqrt

def is_prime(n):
    for i in range(2, int(sqrt(n))):
        if n % i == 0:
            return False
    return True

def prime_factors(n):
    primes = defaultdict(int)
    i = 2
    mx = sqrt(n)
    while n != 1:
        if n % i == 0:
            n = n // i
            primes[i] += 1
        elif i >= mx:
            if len(primes) == 0:
                primes[i] += 1
            elif is_prime(n):
                primes[i] += 1
            break
        else:
            i += 1
    return primes

def solve_n(x):
    return (-1 + sqrt(1 + 4 * 2* x)) / 2

def solve(N: int):
    fs = prime_factors(N)
    count = 0
    for key, value in fs.items():
        val = solve_n(value)
        count += math.floor(val)

    print(count)
    return



# Generated by 1.1.7.1 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word

    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    solve(N)


if __name__ == "__main__":
    main()
Buggy code:
def prime(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return list(set(a))
x=int(input())
p=prime(x)
s=0

for j in p:
    i=1
    while x%(j**i)==0:
        x=x//(j**i)
        s+=1
        i+=1
print(p)
print(s)

Fixed code:
def prime(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return list(set(a))
x=int(input())
p=prime(x)
s=0

for j in p:
    i=1
    while x%(j**i)==0:
        x=x//(j**i)
        s+=1
        i+=1
print(s)
Buggy code:
import math




def solve(n):
    ans = 0
    for i in range(2, int(math.sqrt(n) + 2)):
        if n % i == 0:
            times = 0
            needed = 1
            while n % i ==0:
                times += 1
                if times>= needed:
                    times = 0
                    needed += 1
                    ans += 1
                n //= i
    if not ans==0:
        print(ans)
    else:
        print(1)
    return



n = int(input())
solve(n)


Fixed code:
import math




def solve(n):
    ans = 0
    for i in range(2, int(math.sqrt(n) + 2)):
        if n % i == 0:
            times = 0
            needed = 1
            while n % i ==0:
                times += 1
                if times>= needed:
                    times = 0
                    needed += 1
                    ans += 1
                n //= i
    if not n == 1:
        print(ans+1)
    else:
        print(ans)
    return



n = int(input())
solve(n)
Buggy code:
n = int(input())
N = n
ans = 0
d = 0
i = 2
while n>1 and i*i<=N:
  c = 0
  if n % i == 0:
    d == 1
    while n % i == 0:
      n = int(n / i)
      c += 1

    while c>=Y:
      ans=ans+1
      Y=Y+U
      U=U+1

  i += 1
      
    
if n > 1:
  ans = 1
print(ans)

Fixed code:
n = int(input())
ans = 0
i = 2

while n>1 and i*i<=n:
  if n % i == 0:
    c = 0
    while n % i == 0:
      n = n / i
      c = c + 1
    Y=1
    U=2
    while c>=Y:
      ans=ans+1
      Y=Y+U
      U=U+1

  i = i + 1
      
    
if n > 1:
  ans = 1 + ans

print(ans)
Buggy code:
import math
import collections


def trial_division(n):
    factor = []
    tmp = int(math.sqrt(n)) + 1
    for num in range(2, tmp):
        while n % num == 0:
            n //= num
            if num != 1:
                factor.append(num)
    if not factor:
        return -1
    else:
        factor.append(n)
        return factor


n = int(input())
l = trial_division(n)
if n == 1:
    print(0)
    exit(0)
if l == -1:
    print(n)
    exit(0)
c = collections.Counter(l[:-1])

ans = 0
for k, v in c.items():
    s = 1
    for i in range(1, v):
        if i * (i + 1) <= v * 2:
            s = max(s, i)
    ans += s
print(ans)


Fixed code:
import math
import collections


def trial_division(n):
    factor = []
    tmp = int(math.sqrt(n)) + 1
    for num in range(2, tmp):
        while n % num == 0:
            n //= num
            if num != 1:
                factor.append(num)
    if not factor:
        return -1
    else:
        factor.append(n)
        return factor


n = int(input())
l = trial_division(n)
if n == 1:
    print(0)
    exit(0)
if l == -1:
    print(1)
    exit(0)
if l[len(l) - 1] == 1:
    l = l[:-1]
c = collections.Counter(l)

ans = 0
for k, v in c.items():
    s = 1
    for i in range(1, v):
        if i * (i + 1) <= v * 2:
            s = max(s, i)
    ans += s
print(ans)
Buggy code:
n = int(input())

def pcheck(n):
    if n == 1:
        return False
    else:
        root = int(n ** 0.5)
        for i in range(2, root + 1):
            if n % i == 0:
                return False
        return True

if n == 1:
    print('0')
else:
    rootn = int(n ** 0.5)
    k = 0
    for i in range(2, rootn + 2):
        if n == 1:
            print(k)
            break
        elif n % i == 0:
            j = 1
            p = i
            while n % p == 0:
                k += 1
                n //= p
                j += 1
                p = i ** j
            p //= i
            while n % i == 0:
                if n % p != 0:
                    p //= i
                    continue
                n //= p
        if pcheck(n) == True:
            k += 1
            print(k)
            break
    else:
        print('1')

Fixed code:
n = int(input())

def pcheck(n):
    if n == 1:
        return False
    else:
        root = int(n ** 0.5)
        for i in range(2, root + 1):
            if n % i == 0:
                return False
        return True

if n == 1:
    print('0')
elif n == 6:
    print('2')
elif pcheck(n) == True:
    print('1')
else:
    rootn = int(n ** 0.5)
    k = 0
    for i in range(2, rootn + 2):
        if n == 1:
            print(k)
            break
        elif n % i == 0:
            j = 1
            p = i
            while n % p == 0:
                k += 1
                n //= p
                j += 1
                p = i ** j
            p //= i
            while n % i == 0:
                if n % p != 0:
                    p //= i
                    continue
                n //= p
    else:
        if pcheck(n) == True:
            k += 1
            print(k)
        else:
            print('1')
Buggy code:
import collections

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a


n = int(input())
c = collections.Counter(prime_factorize(n))
l = c.values()
ans=0
for i in list(l):
    temp = i
    j=1
    while temp>0:
        temp -= j
        j += 1
        ans += 1
print(ans)

    


Fixed code:
import collections

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a


n = int(input())
c = collections.Counter(prime_factorize(n))
l = c.values()
ans=0
for i in list(l):
    temp = i
    j=1
    while temp > 0:
        if temp < j:
            break
        temp -= j
        j += 1
        ans += 1
print(ans)
Buggy code:
N = int(input())
if N == 1:
    print("0")
    exit()

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

import collections

c = collections.Counter(prime_factorize(N))

ans = 0
for i in c.keys():
    num = c[i]
    m = 1
    while num > 1:
        num = num - m
        m += 1
        ans += 1

print(ans)

Fixed code:
N = int(input())
if N == 1:
    print("0")
    exit()

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

import collections

c = collections.Counter(prime_factorize(N))

ans = 0
for i in c.keys():
    num = c[i]
    m = 2
    while num > 0:
        num = num - m
        m += 1
        ans += 1

print(ans)
Buggy code:
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(cnt)

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

m = int(input())
a = factorization(m)
ans = 0
for i in a:
    j = 1
    while j *(j+1) //2 <= i:
        j += 1
    ans += j-1
print(ans)


Fixed code:
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

m = int(input())
if m == 1:
  print(0)
  exit()
a = factorization(m)
b = []
ans = 0
for i in a:
    j = 1
    while j *(j+1) //2 <= i[1]:
        j += 1
    ans += j-1
print(ans)
Buggy code:
n = int(input())


def prime_factorize(n):
    res = []
    for i in range(2, int(n ** 0.5) + 1):
        while n % i == 0:
            res.append(i)
            n //= i
    if n != 1:
        res.append(n)
    return res


fac = prime_factorize(n)

from collections import Counter

ctr = Counter(fac)

ans = 0
for val in ctr.values():
    cnt = 1
    while val > 0:
        ans += 1
        val -= cnt
        cnt += 1


print(ans)


Fixed code:
n = int(input())


def prime_factorize(n):
    res = []
    for i in range(2, int(n ** 0.5) + 1):
        while n % i == 0:
            res.append(i)
            n //= i
    if n != 1:
        res.append(n)
    return res


fac = prime_factorize(n)

from collections import Counter

ctr = Counter(fac)

ans = 0
for val in ctr.values():
    cnt = 1
    while val - cnt >= 0:
        ans += 1
        val -= cnt
        cnt += 1


print(ans)
Buggy code:
N = int(input())


def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            arr.append([i, cnt])

    if temp != 1:
        arr.append([temp, 1])

    if arr == []:
        arr.append([n, 1])

    return arr


bunkai = factorization(N)
count = 0

for x in bunkai:
    check = x[1]
    current = 1
    while True:
        check -= current
        if check > 1:
            current += 1
        else:
            break
    count += current
print(count)


Fixed code:
N = int(input())


def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n ** 0.5 // 1)) + 1):
        if temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            arr.append([i, cnt])

    if temp != 1:
        arr.append([temp, 1])

    if arr == []:
        arr.append([n, 1])

    return arr


bunkai = factorization(N)
count = 0

prime_flag = False
for x in bunkai:
    if x[0] == 1:
        prime_flag = True
        break
    else:
        check = x[1]
        current = 2
        while True:
            check -= current
            if check > 0:
                current += 1
            else:
                break
        count += current - 1
if prime_flag:
    print(0)
else:
    print(count)
Buggy code:
n = int(input())
arr = []
temp = n
for i in range(2, int(-(-n**0.5//1))+1):
    if temp%i==0:
        cnt=0
        while temp%i==0:
            cnt+=1
            temp //= i
        arr.append([i, cnt])
if temp!=1:
    arr.append([temp, 1])
if arr==[]:
    arr.append([n, 1])

z = []
for i in arr:
    for j in range(1,i[1]+1):
        z.append(i[0]**j)
z = sorted(set(z))
c = 0
for i in z:
    if n%i == 0:
        c += 1
        n = int(n/i)
print(c) 

Fixed code:
n = int(input())

if n == 1:
    c = 0
else:
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])
    if temp!=1:
        arr.append([temp, 1])
    if arr==[]:
        arr.append([n, 1])
    z = []
    for i in arr:
        for j in range(1,i[1]+1):
            z.append(i[0]**j)
    z = sorted(set(z))
    c = 0
    for i in z:
        if n%i == 0:
            c += 1
            n = int(n/i)
print(c)
Buggy code:
import math
n = int(input())
def prime_factorization(n):
    arr = []
    temp = n
    for i in range(2, int(math.sqrt(temp)) + 1):
        if n%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            if cnt != 0:
                arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr
if n == 1:
    print(0)
elif len(prime_factorization(n)) == 1:
    print(1)
else:
    ans = 0
    prime_list = prime_factorization(n)
    # print(prime_list)
    for i in prime_list:
        a = i[1]
        sub = 1
        j = 0
        while True:
            if a < sub:
                break
            a -= sub
            sub += 1
            j += 1
            
        #     print(a, sub, j)
        # print(j, i[1])
        ans += j
        
    print(ans)

Fixed code:
import math
n = int(input())
def prime_factorization(n):
    arr = []
    temp = n
    for i in range(2, int(math.sqrt(temp)) + 1):
        if n%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            if cnt != 0:
                arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr
if n == 1:
    print(0)
elif len(prime_factorization(n)) == 1 and prime_factorization(n)[0][1] == 1:
    print(1)
else:
    ans = 0
    prime_list = prime_factorization(n)
    # print(prime_list)
    for i in prime_list:
        a = i[1]
        sub = 1
        j = 0
        while True:
            if a < sub:
                break
            a -= sub
            sub += 1
            j += 1
            
        #     print(a, sub, j)
        # print(j, i[1])
        ans += j
        
    print(ans)
Buggy code:
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

n = int(input())
a = factorization(n)

ans = 0
for i in a:
    ans += 1
    k = 2
    l = i[1] - 1
    while l >= k:
        ans += 1
        l -= k
        k += 1
print(ans)

Fixed code:
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

n = int(input())
a = factorization(n)
ans = 0
if n == 1:
    ans = -1
for i in a:
    ans += 1
    k = 2
    l = i[1] - 1
    while l >= k:
        ans += 1
        l -= k
        k += 1
print(ans)