为什么博客园的LaTex有问题啊。

 跑了40s左右，跑得还是有点久……

//waz#include 
     
      using namespace std;#define mp make_pair#define pb push_back#define fi first#define se second#define ALL(x) (x).begin(), (x).end()#define SZ(x) ((int)((x).size()))typedef pair
      
        PII;typedef vector
       
         VI;typedef long long int64;typedef unsigned int uint;typedef unsigned long long uint64;#define gi(x) ((x) = F())#define gii(x, y) (gi(x), gi(y))#define giii(x, y, z) (gii(x, y), gi(z))int F(){    char ch;    int x, a;    while (ch = getchar(), (ch < '0' || ch > '9') && ch != '-');    if (ch == '-') ch = getchar(), a = -1;    else a = 1;    x = ch - '0';    while (ch = getchar(), ch >= '0' && ch <= '9')        x = (x << 1) + (x << 3) + ch - '0';    return a * x;}const int mod = 1e9;int inc(int a, int b) { a += b; return a >= mod ? a - mod : a; }int dec(int a, int b) { a -= b; return a < 0 ? a + mod : a; }const int N = 1e6 + 10;int64 n;int sump[N], sum2[N];int sqrtn;int p[N], m;namespace work1{    int sum(int64 x)    {        int64 y = x + 1;        if (x & 1) y >>= 1; else x >>= 1;        return (x % mod) * (y % mod) % mod;    }    int S(int64 x, int j)    {        if (x < sqrtn && x < 1LL * p[j + 1] * p[j + 1]) return sum2[x];        if (!j) { return dec(sum(x), 1); }        if (1LL * p[j] * p[j] > x) return S(x, j - 1);        else return dec(S(x, j - 1), 1LL * p[j] * dec(S(x / p[j], j - 1), sump[j - 1]) % mod);    }}namespace work2{    const int K = 5000;    unordered_map
        
          ha;    bitset<200010000> s;    int dfs(int64 x, int i)    {        if (!i) return x % mod;        if (!x) return 0;        if (ha[i * n + x]) return ha[i * n + x];        int ans = x % mod;        for (int j = i; j; --j)        {            ans = dec(ans, dfs(x / p[j], j - 1));        }        return ha[i * n + x] = ans;    }    int solve()    {        int ans = 0;        int k = 1;        for (; p[k] < K && k < m; ++k);        //cerr << k << endl;        for (int i = 1; i <= k; ++i)            ans = inc(ans, 1LL * p[i] * (dfs(n / p[i], i - 1) - 1) % mod);        if (k == m) return ans;        int64 ret = n / p[k] - 1;        for (int i = 1; i <= k; ++i)            for (int j = p[i], c = n / p[k]; j <= c; j += p[i])                if (!s[j]) s[j] = 1, --ret;        for (int i = k + 1; i <= m; ++i)        {            int t = n / p[i - 1], tt = n / p[i];            for (int j = t; j > tt; --j)                if (!s[j]) --ret;            ans = inc(ans, ret % mod * p[i] % mod);            for (int j = p[i]; j <= tt; j += p[i])                if (!s[j]) s[j] = 1, --ret;        }        return ans;    }}main(){    cin >> n;    sqrtn = sqrt(n);    static bool fg[N];    for (int i = 2; i <= sqrtn; ++i)    {        if (!fg[i])            p[++m] = i;        for (int j = 1; j <= m && p[j] * i <= sqrtn; ++j)        {            fg[p[j] * i] = 1;            if (i % p[j] == 0) break;        }    }    for (int i = 1; i <= m; ++i) sump[i] = inc(sump[i - 1], p[i]);    for (int i = 2; i <= sqrtn; ++i) sum2[i] = inc(sum2[i - 1], i * (!fg[i]));    int ans2 = work2::solve();    //cerr << "task2 : " << clock() << " ms" << endl;    //cerr << ans2 << endl;    int ans1 = work1::S(n, m);    //cerr << "task1 : " << clock() << " ms" << endl;    //cerr << ans1 << endl;    cout << inc(ans1, ans2) << endl;}