Buggy python submission (verdict: Runtime Error):
from sys import setrecursionlimit; setrecursionlimit(10**9)
N = int(input())

def factorize(n):
    # NOTE: if n == 1, return []
    if n < 1:
        raise Exception('Invalid input: n = {}'.format(n))
    i = 2
    ret = []
    while i * i <= n:
        while n % i == 0:
            n //= i
            ret.append(i)
        i += 1
    if n > 1:
        ret.append(n)
    return ret

A = factorize(N)
l = len(A)

def res(i, B, C):
    if i >= l:
        val = 1
        for b in B:
            val *= b
        C.append(max(len(str(val)), len(str(N//val))))
        return None
    B.append(A[i])
    res(i+1, B, C)
    B.pop()
    res(i+1, B, C)
    return C

C = res(0, [], [])
print(min(C))

Fixed submission:
from sys import setrecursionlimit; setrecursionlimit(10**9)
N = int(input())

def factorize(n):
    # NOTE: if n == 1, return []
    if n < 1:
        raise Exception('Invalid input: n = {}'.format(n))
    i = 2
    ret = []
    while i * i <= n:
        while n % i == 0:
            n //= i
            ret.append(i)
        i += 1
    if n > 1:
        ret.append(n)
    return ret

A = factorize(N)
l = len(A)

def res(i, B, C):
    if i >= l:
        val = 1
        for b in B:
            val *= b
        C.append(max(len(str(val)), len(str(N//val))))
        return None
    B.append(A[i])
    res(i+1, B, C)
    B.pop()
    res(i+1, B, C)
    return C

if N == 1:
    print(1)
else:
    C = res(0, [], [])
    print(min(C))

Buggy python submission (verdict: Runtime Error):
from sys import setrecursionlimit; setrecursionlimit(10**9)
N = int(input())

def factorize(n):
    # NOTE: if n == 1, return []
    if n < 1:
        raise Exception('Invalid input: n = {}'.format(n))
    i = 2
    ret = []
    while i * i <= n:
        while n % i == 0:
            n //= i
            ret.append(i)
        i += 1
    if n > 1:
        ret.append(n)
    return ret

A = factorize(N)
l = len(A)

def res(i, B, C):
    if i >= l:
        val = 1
        for b in B:
            val *= b
        C.append(max(len(str(val)), len(str(N//val))))
        return None
    B.append(A[i])
    res(i+1, B, C)
    B.pop()
    res(i+1, B, C)
    return C

C = res(0, [], [])
print(min(C))

Fixed submission:
from sys import setrecursionlimit; setrecursionlimit(10**9)
N = int(input())

def factorize(n):
    # NOTE: if n == 1, return []
    if n < 1:
        raise Exception('Invalid input: n = {}'.format(n))
    i = 2
    ret = []
    while i * i <= n:
        while n % i == 0:
            n //= i
            ret.append(i)
        i += 1
    if n > 1:
        ret.append(n)
    return ret

A = factorize(N)
l = len(A)

def res(i, B, C):
    if i >= l:
        val = 1
        for b in B:
            val *= b
        C.append(max(len(str(val)), len(str(N//val))))
        return None
    B.append(A[i])
    res(i+1, B, C)
    B.pop()
    res(i+1, B, C)
    return C

if N == 1:
    print(1)
else:
    C = res(0, [], [])
    print(min(C))

Buggy python submission (verdict: Runtime Error):
N = int(input())

def factorize(n):
    # NOTE: if n == 1, return []
    if n < 1:
        raise Exception('Invalid input: n = {}'.format(n))
    i = 2
    ret = []
    while i * i <= n:
        while n % i == 0:
            n //= i
            ret.append(i)
        i += 1
    if n > 1:
        ret.append(n)
    return ret

A = factorize(N)
l = len(A)

def res(i, B, C):
    if i >= l:
        val = 1
        for b in B:
            val *= b
        C.append(max(len(str(val)), len(str(N//val))))
        return None
    B.append(A[i])
    res(i+1, B, C)
    B.pop()
    res(i+1, B, C)
    return C

C = res(0, [], [])
print(min(C))

Fixed submission:
from sys import setrecursionlimit; setrecursionlimit(10**9)
N = int(input())

def factorize(n):
    # NOTE: if n == 1, return []
    if n < 1:
        raise Exception('Invalid input: n = {}'.format(n))
    i = 2
    ret = []
    while i * i <= n:
        while n % i == 0:
            n //= i
            ret.append(i)
        i += 1
    if n > 1:
        ret.append(n)
    return ret

A = factorize(N)
l = len(A)

def res(i, B, C):
    if i >= l:
        val = 1
        for b in B:
            val *= b
        C.append(max(len(str(val)), len(str(N//val))))
        return None
    B.append(A[i])
    res(i+1, B, C)
    B.pop()
    res(i+1, B, C)
    return C

if N == 1:
    print(1)
else:
    C = res(0, [], [])
    print(min(C))