Harryxun/sft_time huggingface dataset:
### BUGGY CODE ###

from collections import Counter
class Prime:
    def __init__(self, N):
        smallestPrime = [i for i in range(N + 1)]

        for i in range(2, N + 1):
            if smallestPrime[i] != i:
                continue
            for p in range(i * 2, N + 1, i):
                if smallestPrime[p] == p:
                    smallestPrime[p] = i

        self.smallestPrime = smallestPrime

    def isPrime(self, n):
        return n > 1 and self.smallestPrime[n] == n

    def factorization(self, n):
        ret = Counter()
        while n > 1:
            p = self.smallestPrime[n]
            ret[p] += 1
            n //= p
        return ret

N = int(input())
prime = Prime(N + 100)

ans = 0
for c in range(1, N):
    cnt = 1
    for c in prime.factorization(N - c).values():
        cnt *= c + 1
    ans += cnt
print(ans)


### FIXED CODE ###

from collections import Counter
class Prime:
    def __init__(self, N):
        smallestPrime = [i for i in range(N + 1)]

        for i in range(2, N + 1):
            if smallestPrime[i] != i:
                continue
            for p in range(i * 2, N + 1, i):
                if smallestPrime[p] == p:
                    smallestPrime[p] = i

        self.smallestPrime = smallestPrime

    def isPrime(self, n):
        return n > 1 and self.smallestPrime[n] == n

    def factorization(self, n):
        ret = Counter()
        while n > 1:
            p = self.smallestPrime[n]
            ret[p] += 1
            n //= p
        return ret

N = int(input())
prime = Prime(N + 100)

ans = 0
for c in range(1, N):
    cnt = 1
    for c in prime.factorization(N - c).values():
        cnt *= c + 1
    ans += cnt
print(ans)
### BUGGY CODE ###

import heapq
N = int( input())
A = list( map( int, input().split()))
fsum = [0]*(N+1)
bsum = [0]*(N+1)
forward = A[:N]
back = A[2*N:]
back = list(map( lambda x:-x, back))
heapq.heapify(forward)
heapq.heapify(back)
fsum[0] = sum(forward)
bsum[N] = -sum(back)
for i in range(1,N+1):
    heapq.heappushpop(forward, A[N+i-1])
    fsum[i] = sum(forward)
    heapq.heappushpop(back, -A[2*N-i])
    bsum[N-i] = -sum(back)
ans = fsum[0] - bsum[0]
for i in range(1,N+1):
    ans = max(ans, fsum[i] - bsum[i])
print(ans)

### FIXED CODE ###

import heapq
N = int( input())
A = list( map( int, input().split()))
fsum = [0]*(N+1)
bsum = [0]*(N+1)
forward = A[:N]
back = A[2*N:]
back = list(map( lambda x:-x, back))
heapq.heapify(forward)
heapq.heapify(back)
fsum[0] = sum(forward)
fsumnow = fsum[0]
bsum[N] = -sum(back)
bsumnow = bsum[N]
for i in range(1,N+1):
    heapq.heappush(forward, A[N+i-1])
    fsumnow += A[N+i-1]
    fsumnow -= heapq.heappop(forward)
    fsum[i] = fsumnow
    heapq.heappush(back, -A[2*N-i])
    bsumnow += A[2*N-i]
    bsumnow += heapq.heappop(back)
    bsum[N-i] = bsumnow
ans = fsum[0] - bsum[0]
for i in range(1,N+1):
    ans = max(ans, fsum[i] - bsum[i])
print(ans)
### BUGGY CODE ###

S=str(input())
Q=int(input())
count=0
for i in range(Q):
	a=list(map(str,input().split()))
	if a[0]=="1":
		count+=1
	elif a[0]=="2":
		if count%2==0:
			if a[1]=="1":
				S=a[2]+S
			elif a[1]=="2":
				S=S+a[2]
		elif count%2==1:
			if a[1]=="1":
				S=S+a[2][::-1]
			elif a[1]=="2":
				S=a[2][::-1]+S
if count%2==1:
	print(S[::-1])
else:
	print(S)

### FIXED CODE ###

S=str(input())
Q=int(input())
count=0
M=''
U=''
for i in range(Q):
	a=list(map(str,input().split()))
	if a[0]=="1":
		count+=1
	elif a[0]=="2":
		if count%2==0:
			if a[1]=="1":
				M=a[2]+M
			elif a[1]=="2":
				U=U+a[2]
		elif count%2==1:
			if a[1]=="1":
				U=U+a[2][::-1]
			elif a[1]=="2":
				M=a[2][::-1]+M
S=M+S+U
if count%2==1:
	print(S[::-1])
else:
	print(S)
### BUGGY CODE ###

def f(h, w):
    t = [input() for _ in range(h)]
    U = [[0] * (w + 2) for _ in range(h + 2)]
    D = [[0] * (w + 2) for _ in range(h + 2)]
    L = [[0] * (w + 2) for _ in range(h + 2)]
    R = [[0] * (w + 2) for _ in range(h + 2)]
    ans = 0
    Ui1 = U[0]
    for i in range(1, 1 + h):
        Ui = U[i]
        Li = L[i]
        ti1 = t[i - 1]
        for j, tk in enumerate(ti1):
            j += 1
            if tk == "#":
                Ui[j] = 0
                Li[j] = 0
            else:
                Ui[j] = Ui1[j] + 1
                Li[j] = Li[j - 1] + 1
        Ui1 = Ui
        Di1 = D[-1]
    for i in range(h, 0, -1):
        Ui = U[i]
        Li = L[i]
        Di = D[i]
        Ri = R[i]
        ti1 = t[i - 1]
        for j in range(w, 0, -1):
            if ti1[j - 1] == "#":
                Di[j] = 0
                Ri[j] = 0
            else:
                Di[j] = Di1[j] + 1
                Ri[j] = Ri[j + 1] + 1
                tmp = Ui[j] + Di[j] + Li[j] + Ri[j]
                if tmp > ans:
                    ans = tmp
        Di1 = Di
    print(ans - 3)

h, w = map(int, input().split())
f(h, w)


### FIXED CODE ###

def f(h, w):
    t = [input() for _ in range(h)]
    U = [[0] * (w + 2) for _ in range(h + 2)]
    D = [[0] * (w + 2) for _ in range(h + 2)]
    L = [[0] * (w + 2) for _ in range(h + 2)]
    R = [[0] * (w + 2) for _ in range(h + 2)]
    ans = 0
    Ui1 = U[0]
    for i in range(1, 1 + h):
        Ui = U[i]
        Li = L[i]
        ti1 = t[i - 1]
        for j, tk in enumerate(ti1):
            j += 1
            if tk == "#":
                Ui[j] = 0
                Li[j] = 0
            else:
                Ui[j] = Ui1[j] + 1
                Li[j] = Li[j - 1] + 1
        Ui1 = Ui
        Di1 = D[-1]
    for i in range(h, 0, -1):
        Ui = U[i]
        Li = L[i]
        Di = D[i]
        Ri = R[i]
        ti1 = t[i - 1]
        for j in range(w, 0, -1):
            if ti1[j - 1] == "#":
                Di[j] = 0
                Ri[j] = 0
            else:
                Di[j] = Di1[j] + 1
                Ri[j] = Ri[j + 1] + 1
                tmp = Ui[j] + Di[j] + Li[j] + Ri[j]
                if tmp > ans:
                    ans = tmp
        Di1 = Di
    print(ans - 3)

h, w = map(int, input().split())
f(h, w)
### BUGGY CODE ###

N = int(input())
a_list = [None] * N
for i in range(N):
    a_list[i] = int(input())

#remove duplicate
sorted_a = sorted(a_list, reverse = True)
max_a = sorted_a[0]

result = []
for a in a_list:
    if a == max_a:
        print(max(sorted_a[1:]))
    else:
        print(max_a)


### FIXED CODE ###

N = int(input())
a_list = [None] * N
for i in range(N):
    a_list[i] = int(input())

#remove duplicate
sorted_a = sorted(a_list, reverse = True)
max_a = sorted_a[0]

result = []
for a in a_list:
    if a == max_a:
        print(sorted_a[1])
    else:
        print(max_a)
### BUGGY CODE ###

from queue import Queue
INF = -1
H, W = map(int,input().split())
MAP = [list(input()) for _ in range(H)]
d = [[INF for i in range(W)] for j in range(H)]
tx = [1, 0, -1, 0]
ty = [0, 1, 0, -1]

q = Queue()
for i in range(H):
    for j in range(W):
        if MAP[i][j] == '#':
            d[i][j] = 0
            q.put([i, j, 0])

ans = 0

while not q.empty():
    p = q.get()
    ans = max(ans, p[2])
    for i in range(4):
        nx = p[0] + tx[i]
        ny = p[1] + ty[i]
        if 0 <= nx <= H-1 and 0 <= ny <= W-1 and d[nx][ny] == INF:
            d[nx][ny] = p[2] + 1
            q.put([nx, ny, p[2]+1])

print(ans)

### FIXED CODE ###

from collections import deque
INF = -1
H, W = map(int,input().split())
d = [[INF for i in range(W)] for j in range(H)]
tx = [1, 0, -1, 0]
ty = [0, 1, 0, -1]

q = deque()
for i in range(H):
    line = list(input())
    for j in range(W):
        if line[j] == '#':
            d[i][j] = 0
            q.append([i, j, 0])

ans = 0

while len(q) > 0:
    p = q.popleft()
    ans = max(ans, p[2])
    for i in range(4):
        nx = p[0] + tx[i]
        ny = p[1] + ty[i]
        if 0 <= nx <= H-1 and 0 <= ny <= W-1 and d[nx][ny] == INF:
            d[nx][ny] = p[2] + 1
            q.append([nx, ny, p[2]+1])

print(ans)
### BUGGY CODE ###

n = int(input())
a = list(map(int, input().split()))

ans = 0
mod = 10**9+7

for i in range(n-1):
    for j in range(i+1,n):
        ans += a[i]*a[j]
        ans %= mod

print(ans)


### FIXED CODE ###

n = int(input())
a = list(map(int, input().split()))

ans = 0
mod = 10**9+7

S = sum(a)

for i in range(n-1):
    S -= a[i]
    ans += a[i]*S
    ans %= mod
print(ans)
### BUGGY CODE ###

import copy

n = int(input())
a_list = []

for i in range(n):
    a_list.append(int(input()))
    
#print(a_list)    
for i in range(n):
    a_copy = copy.copy(a_list)
    a_copy.pop(i)
    #print(a_copy)
    print(max(a_copy))

### FIXED CODE ###


n = int(input())
a = []

for i in range(n):
    a.append(int(input()))
    
a_copy = list(a)
a.sort(reverse=True)

max_1 = a[0]
max_count = a.count(max_1)

for i in a:
    if i < max_1:
        max_2 = i
        break
        
for a in a_copy:
    if a == max_1 and max_count == 1:
        print(max_2)
    else:
        print(max_1)
### BUGGY CODE ###

import sys
sys.setrecursionlimit(500000)

n, m = map(int, input().split())
edges = [[] for _ in range(n)]
for i in range(m):
    l, r, d = map(int, input().split())
    l -= 1
    r -= 1
    edges[l].append((r, d))
    edges[r].append((l, -d))


coord = [None for i in range(n)]
def dfs(v):
    possible = True
    for u, d in edges[v]:
        if coord[u]:
            if coord[u] != coord[v] + d:
                return False
        else:
            # not visited yet
            coord[u] = coord[v] + d
            possible = possible and dfs(u)

    return possible

ans = True
for i in range(n):
    if coord[i]:
        continue
    coord[i] = 0
    ans = ans and dfs(i)

if ans:
    print("Yes")
else:
    print("No")


### FIXED CODE ###

from collections import deque

def topological_sort(graph: list, n_v: int) -> list:
    # graph[node] = [(cost, to)]
    indegree = [0] * n_v # 各頂点の入次数
    for i in range(n_v):
        for c, v in graph[i]:
            indegree[v] += 1

    cand = deque([i for i in range(n_v) if indegree[i] == 0])
    res = []
    while cand:
        v1 = cand.popleft()
        res.append(v1)
        for c, v2 in graph[v1]:
            indegree[v2] -= 1
            if indegree[v2] == 0:
                cand.append(v2)

    return res




n, m = map(int, input().split())
edges = [[] for _ in range(n)]
for i in range(m):
    l, r, d = map(int, input().split())
    l -= 1
    r -= 1
    edges[l].append((d, r))

ts = topological_sort(edges, n)

if len(ts) != n:
    ans = "No"
    # print("Not DAG")
else:
    # DAG
    dist = [-1] * n
    ans = "Yes"
    for i in range(n):
        v = ts[i]
        if dist[v] == -1:
            dist[v] = 0

        for c, u in edges[v]:
            if dist[u] == -1:
                dist[u] = dist[v] + c
            elif dist[u] != dist[v] + c:
                ans = "No"
                break

print(ans)
### BUGGY CODE ###

from networkx import*
def main():
    g=Graph()
    for a in[*open(x:=0)][1:]:
        a,b=map(int,a.split())
        g.add_edge(a,7**6+b)
    for c in connected_components(g):
        a,b=map(len,bipartite.sets(s:=g.subgraph(c)))
        x+=a*b-len(s.edges)
    print(x)
main()

### FIXED CODE ###

class UnionFind():
    def __init__(self,size):
        self.table=[-1]*size
    def root(self,x):
        while self.table[x]>=0:
            x=self.table[x]
        return x
    def unite(self,x,y):
        s1=self.root(x)
        s2=self.root(y)
        if s1!=s2:
            if self.table[s1]>self.table[s2]:
                s1,s2=s2,s1
            self.table[s1]+=self.table[s2]
            self.table[s2]=s1
        return
    def same(self,x,y):
        return self.root(x)==self.root(y)
    def size(self,x):
        return -self.table[self.root(x)]
n,*z=map(int,open(0).read().split())
u=UnionFind(10**5*2+1)
for x,y in zip(*[iter(z)]*2):
    u.unite(x,10**5+y)
d=[[0,set(),set()]for _ in range(10**5*2+1)]
for x,y in zip(*[iter(z)]*2):
    t=d[u.root(x)]
    t[0]+=1
    t[1].add(x)
    t[2].add(y)
print(sum(len(x)*len(y)-a for a,x,y in d))
### BUGGY CODE ###

from collections import Counter

def solve():
    MOD = 10**9 + 7

    def getPrimeFactors(x):
        anss = []
        for d in range(2, int(x**0.5)+1):
            while x%d == 0:
                anss.append(d)
                x //= d
        if x != 1:
            anss.append(x)
        return anss

    N = int(input())
    As = list(map(int, input().split()))

    PFss = []
    Primes = set()
    for A in As:
        PFs = getPrimeFactors(A)
        cnt = Counter(PFs)
        PFss.append(cnt)
        Primes |= cnt.keys()

    lcmA = 1
    for P in Primes:
        num = 0
        for PFs in PFss:
            if PFs[P] > num:
                num = PFs[P]
        lcmA *= pow(P, num, MOD)
        lcmA %= MOD

    def getInvs(n, MOD):
        invs = [1] * (n+1)
        for x in range(2, n+1):
            invs[x] = (-(MOD//x) * invs[MOD%x]) % MOD
        return invs

    invs = getInvs(10**6, MOD)

    ans = 0
    for A in As:
        ans += lcmA * invs[A]
        ans %= MOD

    print(ans)

solve()


### FIXED CODE ###

from collections import Counter

def solve():
    MOD = 10**9 + 7
    maxA = 10**6

    N = int(input())
    As = list(map(int, input().split()))

    isPrimes = [False]*2 + [True]*(maxA-1)
    minFs = [1] * (maxA+1)
    for i in range(2, int(maxA**0.5) + 1):
        if isPrimes[i]:
            for x in range(i*i, maxA+1, i):
                isPrimes[x] = False
                minFs[x] = i

    def getPrimeFactors(x):
        anss = []
        while minFs[x] > 1:
            anss.append(minFs[x])
            x //= minFs[x]
        if x != 1:
            anss.append(x)
        return anss

    PFss = []
    Primes = set()
    for A in As:
        PFs = getPrimeFactors(A)
        cnt = Counter(PFs)
        PFss.append(cnt)
        Primes |= cnt.keys()

    cntP = Counter()
    for PFs in PFss:
        for key, num in PFs.items():
            cntP[key] = max(cntP[key], num)

    lcmA = 1
    for key, num in cntP.items():
        lcmA *= pow(key, num, MOD)
        lcmA %= MOD

    def getInvs(n, MOD):
        invs = [1] * (n+1)
        for x in range(2, n+1):
            invs[x] = (-(MOD//x) * invs[MOD%x]) % MOD
        return invs

    invs = getInvs(10**6, MOD)

    ans = 0
    for A in As:
        ans += lcmA * invs[A]
        ans %= MOD

    print(ans)

solve()
### BUGGY CODE ###

import math
k = int(input())
ans = 0
for i in range(1, k + 1):
    for j in range(1, k + 1):
        for l in range(1, k + 1):
            ans += math.gcd(math.gcd(i, j), l)
print(ans)

### FIXED CODE ###

import math
k = int(input())
ans = 0
for i in range(1, k + 1):
    for j in range(1, k + 1):
        for l in range(1, k + 1):
            ans += math.gcd(math.gcd(i, j), l)
print(ans)
### BUGGY CODE ###

import sys
input = sys.stdin.readline
def main():
  n=int(input())
  s=str(input())
  r=[]
  g=[]
  b=[]
  for i in range(n):
    if s[i]=='R':
      r.append(i)
    elif s[i]=='G':
      g.append(i)
    else:
      b.append(i)
  ans=0
  for l in r:
    for m in g:
      for k in b:
        if abs(m-l)!=abs(k-m) and abs(k-l)!=abs(k-m) and abs(k-l)!=abs(l-m):
          ans+=1
  print(ans)
main()

### FIXED CODE ###

n=int(input())
s=str(input())
if n<=2:
    print(0)
    exit()
r=s.count('R')
g=s.count('G')
b=s.count('B')
ans=r*g*b
for i in range(n-2):
    for j in range(i+1,n-1):
        if 2*j-i>n-1:
            break
        if s[i]!=s[j] and s[j]!=s[2*j-i] and s[i]!=s[2*j-i]:
            ans-=1
print(ans)
### BUGGY CODE ###

import numpy as np
from collections import deque


def p_e():
    n, k = map(int, input().split())
    *a, = map(int, input().split())
    dp = np.array([0] * n)
    q = deque()
    ans = 0
    for i in range(n):
        q.appendleft(i + 1)
        c = a[i] % k
        now_dp = dp[:i + 1]
        now_dp += c
        now_dp %= k
        ans += np.sum(now_dp == q)
    print(ans)

p_e()

### FIXED CODE ###


from collections import deque
from collections import defaultdict


def p_e():
    n, k = map(int, input().split())
    a = [0] + list(map(int, input().split()))
    for i in range(n):
        a[i + 1] = (a[i + 1] + a[i] - 1) % k
    d = defaultdict(int)
    d[0] = 1
    q = deque()
    ans = 0
    for i in range(1, n + 1):
        if i - k >= 0:
            d[a[i - k]] -= 1
        ans += d[a[i]]
        d[a[i]] += 1
    print(ans)
    
p_e()
### BUGGY CODE ###

class SegTree:

    def __init__(self, N):
        self.N = N
        self.data = [0 for _ in range(2 * N)]

    def update(self, i, x):
        index = self.N + i - 1
        self.data[index] = x
        while index > 0:
            index = (index - 1) // 2  # parent
            self.data[index] = max(self.data[2 * index + 1], self.data[2 * index + 2])

    def _query(self, a, b, k, l, r):
        if r <= a or b <= l:
            return 0
        if a <= l and r <= b:
            return self.data[k]
        else:
            vl = self._query(a, b, 2 * k + 1, l, (l + r) // 2)
            vr = self._query(a, b, 2 * k + 2, (l + r) // 2, r)
            return max(vl, vr)

    def query(self, a, b):
        return self._query(a, b, 0, 0, self.N)


def main():
    chars = [chr(ord('a') + i) for i in range(26)]
    N = int(input())
    pw2 = 1
    while pw2 < N:
        pw2 *= 2
    S = input()
    Q = int(input())
    query_list = [input().split(' ') for _ in range(Q)]
    trees = dict()
    for c in chars:
        trees[c] = SegTree(pw2)
    for i, c in enumerate(S):
        trees[c].update(i, 1)
    for query in query_list:
        if query[0] == '1':
            # type 1 query
            i = int(query[1]) - 1
            new_c = query[2]
            for c in chars:
                x = (1 if c == new_c else 0)
                trees[c].update(i, x)
        else:
            # type 2 query
            left = int(query[1]) - 1
            right = int(query[2]) - 1
            kinds = sum([trees[c].query(left, right + 1) for c in chars])
            print(kinds)


if __name__ == '__main__':
    main()


### FIXED CODE ###

class BIT:

    def __init__(self, N):
        # NOTE: 1-indexed
        self.N = N
        self.data = [0] * (N + 1)

    def sum(self, i):
        s = 0
        while i > 0:
            s += self.data[i]
            i -= i & (- i)
        return s

    def update(self, i, x):
        while i <= self.N:
            self.data[i] += x
            i += i & (- i)


def c2n(c):
    return ord(c) - ord('a')


def main():
    N = int(input())
    S = input()
    char_list = list(S)
    trees = [BIT(N) for _ in range(26)]
    for i, c in enumerate(S):
        trees[c2n(c)].update(i + 1, 1)
    Q = int(input())
    ans = list()
    for _ in range(Q):
        query = input().split()
        if query[0] == '1':
            _, i, c = query
            i = int(i) - 1
            before_c = char_list[i]
            char_list[i] = c
            trees[c2n(before_c)].update(i + 1, - 1)
            trees[c2n(c)].update(i + 1, 1)
        else:  # type '2'
            _, left, right = query
            left, right = int(left) - 1, int(right) - 1
            cnt = 0
            for i in range(26):
                n = trees[i].sum(right + 1) - trees[i].sum(left)
                if n > 0:
                    cnt += 1
            ans.append(cnt)
    for a in ans:
        print(a)


if __name__ == '__main__':
    main()
### BUGGY CODE ###

import sys
import collections
input = lambda: sys.stdin.readline().rstrip()

def main():
    n = int(input())
    s = [input() for _ in range(n)]
    cnt = collections.Counter(s)
    d = [k for k, v in cnt.items() if v == max(cnt.values())]
    d = sorted(d)
    for i in d:
        print(i)    

if __name__ == '__main__':
    main()

### FIXED CODE ###

import sys
import collections
input = lambda: sys.stdin.readline().rstrip()

def main():
    n = int(input())
    s = [input() for _ in range(n)]
    cnt = collections.Counter(s)
    values, counts = zip(*cnt.most_common())
    d = sorted(values[:counts.count(counts[0])])
    print(*d, sep='\n')

if __name__ == '__main__':
    main()
### BUGGY CODE ###

s=input()
ans=0
num=0
while num<len(s)-1:
    if s[num]!=s[num+1]:
        s=s[:num]+s[num+2:]
        num-=1
        ans+=2
    else:
        num+=1
print(ans)

### FIXED CODE ###

s=input()
print(2*min(s.count("0"), s.count("1")))
### BUGGY CODE ###

N = int(input())
S = input()


"""考え方
「右側のE」+「左側のW」の合計が一番小さくなるインデックスを探索する。
"""

ans = 10**6
## 西の端から東に向かって確認していく
for n in range(0,N):
  cnt = S[:n].count('W') + S[n:].count('E')
  ans = min(ans,cnt)

print(ans)

### FIXED CODE ###

N = int(input())
S = input()


"""考え方
「右側のE」+「左側のW」の合計が一番小さくなるインデックスを探索する。
"""
left_w = 0
right_e = S.count('E')
ans = 10**6
## 西の端から東に向かって確認していく
for n in range(0,N):
  if S[n] == "W":
    cnt = left_w + right_e
    left_w += 1
  else:
    cnt = left_w + right_e - 1
    right_e -= 1
    
  ans = min(ans,cnt)

print(ans)
### BUGGY CODE ###

import sys
def slove(n, t):
    t.sort()
    max_num = t.pop()
    i = 1
    while True:
        ans = max_num * i
        tmp = all([True if ans % j == 0 else False for j in t])
        if tmp:
            break
        else:
            i += 1

    return ans

if __name__ == "__main__":
    input = sys.stdin.readline
    n = int(input())
    t = [int(input()) for i in range(n)]
    print(slove(n, t))


### FIXED CODE ###

import sys
import functools
import fractions
def slove(n, t):
    t.sort()
    ans = functools.reduce(lambda x,y:(x*y)//fractions.gcd(x,y), t)
    return ans

if __name__ == "__main__":
    input = sys.stdin.readline
    n = int(input())
    t = [int(input()) for i in range(n)]
    print(slove(n, t))
### BUGGY CODE ###

N = int(input())
A = [0] + [int(_) for _ in input().split()]
B = [0]
is_monotone = True
for i in range(N):
    if is_monotone:
        is_monotone &= A[i + 1] > A[i]
    B += [min(A[i + 1], 18)]
if is_monotone:
    print(1)
    exit()


def is_possible(K):
    dp = [0] * 18
    for i in range(N):
        if B[i] >= B[i + 1]:
            dp = dp[:B[i + 1]] + [0] * (19 - B[i + 1])
            flag = True
            for j in range(B[i + 1] - 1, -1, -1):
                if dp[j] < K - 1:
                    dp[j] += 1
                    flag = False
                    break
                else:
                    dp[j] = 0
            if flag:
                return False
    return True


def bis(x, y):
    if y == x + 1:
        return y
    elif is_possible((x + y) // 2):
        return bis(x, (x + y) // 2)
    else:
        return bis((x + y) // 2, y)


print(bis(0, N))


### FIXED CODE ###

import random
input()
A = [int(_) for _ in input().split()]
A = [A[0]] + [j for i, j in zip(A, A[1:]) if i >= j]
N = len(A)


def cut(array, index):
    if index < 1:
        return []
    if index <= array[0][0]:
        return [(index, array[0][1])]
    for _ in range(len(array)-1, 0, -1):
        if array[_ - 1][0] < index:
            return array[:_] + [(index, array[_][1])]


def is_possible(K):
    dp = [(A[0], 0)]
    for a in A[1:]:
        if a <= dp[-1][0]:
            dp = cut(dp, a)
        else:
            dp += [(a, 0)]
        is_added = False
        for j in range(len(dp) - 1, -1, -1):
            if dp[j][1] < K - 1:
                dp = cut(dp, dp[j][0] - 1) + [(dp[j][0], dp[j][1] + 1)]
                if dp[-1][0] < a:
                    dp += [(a, 0)]
                is_added = True
                break
        if not is_added:
            return False
    return True


def bis(x, y):
    if y == x + 1:
        return y
    elif is_possible((x + y) // 2):
        return bis(x, (x + y) // 2)
    else:
        return bis((x + y) // 2, y)


print(bis(0, N))
### BUGGY CODE ###

import math
from functools import reduce
def gcd(*numbers):
    return reduce(math.gcd, numbers)

K=int(input())
ans=0
for a in range(1,K+1):
    for b in range(1, K + 1):
        for c in range(1,K+1):
            ans+=gcd(a,b,c)
print(ans)

### FIXED CODE ###

import math
from functools import reduce
def gcd(*numbers):
    return reduce(math.gcd, numbers)

K=int(input())
ans=0
for a in range(1,K+1):
    for b in range(1, K + 1):
        for c in range(1,K+1):
            ans+=gcd(a,b,c)
print(ans)