import sys
import math

def solve():
    input_data = sys.stdin.read().split()
    if not input_data:
        return
    N = int(input_data[0])
    MOD = 998244353

    def F(X):
        if X <= 0: return 0
        M = math.isqrt(X)
        n = M - 1
        S2 = n * (n + 1) * (2 * n + 1) // 6
        S3 = (n * (n + 1) // 2) ** 2
        S4 = n * (n + 1) * (2 * n + 1) * (3 * n * n + 3 * n - 1) // 30
        ans = 2 * S4 + 3 * S3 + S2
        rem_sum = (X + M * M) * (X - M * M + 1) // 2
        ans += M * rem_sum
        return ans % MOD

    MAX_INV = 1000005
    inv = [0] * MAX_INV
    inv[1] = 1
    for i in range(2, MAX_INV):
        inv[i] = MOD - (MOD // i) * inv[MOD % i] % MOD

    events = {}
    for k in range(3, 60):
        x = 2
        while True:
            v = x ** k
            if v > N:
                break
            if v not in events:
                events[v] = []
            events[v].append(x)
            x += 1

    sorted_v = sorted(events.keys())

    curr_v = 1
    ans = 0
    H = 1

    for v in sorted_v:
        if v > curr_v:
            val = (F(v - 1) - F(curr_v - 1)) % MOD
            ans = (ans + H * val) % MOD
        for x in events[v]:
            H = (H * x) % MOD
            H = (H * inv[x - 1]) % MOD
        curr_v = v

    if curr_v <= N:
        val = (F(N) - F(curr_v - 1)) % MOD
        ans = (ans + H * val) % MOD

    print(ans)

if __name__ == '__main__':
    solve()