$x^x$ 的位数为 $x\times \log_{10}{x}$

#include <bits/stdc++.h>
#define int long long
using namespace std;
int n;
// 返回 x^x 的位数
int f(int x)
{
    return x * log10(x) + 1;
}
signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> n;
    int l = 1;
    int r = 2'000'000'000;
    int ans = -1;
    while (l <= r)
    {
        int mid = (l + r) / 2;
        if (f(mid) >= n)
        {
            ans = mid;
            r = mid - 1;
        }
        else
            l = mid + 1;
    }
    cout << ans << "\n";
    return 0;
}