1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
| #include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 100;
const int mod = 998244353;
int qpow(int a, int b) {
int ret = 1;
while (b) {
if (b & 1) ret = 1ll * ret * a % mod;
a = 1ll * a * a % mod;
b >>= 1;
}
return ret;
}
int facinv[maxn] = {1, 1};
void facinv_ini() {
for (int i = 0, fac = 1; i < maxn; ++i, fac = 1ll * fac * i % mod) {
facinv[i] = qpow(fac, mod - 2);
}
}
int lagrange(int *y, int n, int x) {
static int prepre[maxn], suf[maxn], *pre = prepre + 1;
pre[-1] = suf[n + 1] = 1;
for (int i = 0; i <= n; ++i) pre[i] = 1ll * pre[i - 1] * (x - i + mod) % mod;
for (int i = n; i >= 0; i--) suf[i] = 1ll * suf[i + 1] * (i - x + mod) % mod;
int b = 0;
for (int i = 0; i <= n; ++i) {
int up = 1ll * pre[i - 1] * suf[i + 1] % mod;
int down = 1ll * facinv[i] * facinv[n - i] % mod;
b = (b + 1ll * y[i] * up % mod * down) % mod;
}
return b;
}
int sum(int n, int I, ll mx) {
static int f[100];
f[0] = 0;
f[1] = (1ll * (n + 1) * (I + 1) % mod - (I + 1) + mod) % mod;
for (int x = 2; x <= I + 3; x++) {
int left = 1ll * (n + 1) * (I + 1) % mod * x % mod;
int fenzi = (qpow(x, 2) - qpow(x, I + 3) + mod) % mod;
int fenmu = (1 - x + mod) % mod;
f[x] = (left - 1ll * fenzi * qpow(fenmu, mod - 2) % mod + mod) % mod;
}
for (int x = 1; x <= I + 3; x++) {
f[x] = (f[x - 1] + f[x]) % mod;
}
return lagrange(f, I + 3, mx % mod);
}
ll _n;
int f(ll x) {
__int128 prod = x;
int res = 0;
while (prod * x <= _n) {
prod *= x;
res++;
}
return res;
}
ll calcEnd(ll l, ll r) {
while (l < r) {
ll mid = (l + r + 1) / 2;
if (f(l) == f(mid)) {
l = mid;
} else {
r = mid - 1;
}
}
return l;
}
int solve(ll n) {
int ans = 0;
for (ll l = 2, r; l <= n; l = r + 1) {
r = calcEnd(l, n);
int I = f(l);
int add = (sum(n % mod, I, r) - sum(n % mod, I, l - 1) + mod) % mod;
ans = (ans + add) % mod;
}
return ans;
}
int main() {
facinv_ini();
ll n;
while (cin >> n) {
_n = n;
for (int i = 0; i < 1e3; i++) {
solve(n);
}
printf("%d\n", solve(n));
}
}
|
