import sys
import math

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

    inv2 = pow(2, MOD - 2, MOD)
    inv6 = pow(6, MOD - 2, MOD)
    inv30 = pow(30, MOD - 2, MOD)

    def F(X):
        if X <= 0: return 0
        M = math.isqrt(X)
        n = (M - 1) % MOD
        
        S2 = n * (n + 1) % MOD * (2 * n + 1) % MOD * inv6 % MOD
        
        v = n * (n + 1) % MOD * inv2 % MOD
        S3 = v * v % MOD
        
        term4 = (3 * n * n % MOD + 3 * n - 1) % MOD
        S4 = n * (n + 1) % MOD * (2 * n + 1) % MOD * term4 % MOD * inv30 % MOD
        
        ans = (2 * S4 + 3 * S3 + S2) % MOD
        
        X_mod = X % MOD
        M_mod = M % MOD
        M2_mod = M_mod * M_mod % MOD
        
        rem_count = (X_mod - M2_mod + 1 + MOD) % MOD
        rem_sum = (X_mod + M2_mod) * rem_count % MOD * inv2 % MOD
        
        ans = (ans + M_mod * rem_sum) % MOD
        return ans

    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
            events.append((v, x))
            x += 1

    events.sort(key=lambda item: item[0])

    curr_v = 1
    ans = 0
    H = 1

    idx = 0
    L = len(events)
    while idx < L:
        v = events[idx][0]
        if v > curr_v:
            val = (F(v - 1) - F(curr_v - 1)) % MOD
            ans = (ans + H * val) % MOD
            curr_v = v
        
        while idx < L and events[idx][0] == v:
            x = events[idx][1]
            H = H * x % MOD * inv[x - 1] % MOD
            idx += 1

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

    print((ans % MOD + MOD) % MOD)

if __name__ == '__main__':
    solve()