// Problem: E2. Rudolf and Snowflakes (hard version)
// Contest: Codeforces - Codeforces Round 883 (Div. 3)
// URL: https://codeforces.com/problemset/problem/1846/E2
// Memory Limit: 256 MB
// Time Limit: 2000 ms
//
// Powered by CP Editor (https://cpeditor.org)

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
const ll maxn = 1000000000000000000;

vector<ll> nums;

ll qpow(ll a, ll b)
{
    ll ans = 1;
    while (b)
    {
        if (b & 1)
        {
            ans *= a;
            if (ans > maxn)
                return INT64_MIN;
        }
        if (a > 1000000000)
            return INT64_MIN;
        a *= a;
        b >>= 1;
    }
    return ans;
}

void solve()
{
    for (ll i = 2; i <= 1000000; i++)
    {
        ll num1 = i - 1;
        // cout << "-----------"
        //     << "\n";
        // cout << "the i: " << i << " the num1: " << num1 << "\n";
        long double t = log(maxn);
        long double t2 = log(i);
        for (ll j = 2; j < (ll)(t / t2); j++)
        {
            // cout << "the j: " << j << "\n";
            ll s = qpow(i, j + 1);
            if (s == INT64_MIN)
                continue;
            // cout << "the sum: " << s - 1 << "\n";
            if ((s - 1) % num1 == 0)
            {
                // cout << "ok"
                //   << "\n";
                // cout << (j == 2 ? i : 114514) << "\n";
                nums.push_back((s - 1) / num1);
            }
        }
    }

    sort(nums.begin(), nums.end());
    nums.erase(unique(nums.begin(), nums.end()), nums.end());
}

bool bs(ll n)
{
    ll l = 0, r = nums.size() - 1, mid;
    while (l < r)
    {
        mid = l + r >> 1;
        if (nums[mid] == n)
            return true;
        else if (n > nums[mid])
            l = mid + 1;
        else
            r = mid;
    }
    return false;
}

int main()
{
    int t;
    cin >> t;
    solve();
    while (t--)
    {
        ll n;
        cin >> n;
        if (n < 3)
        {
            cout << "NO"
                 << "\n";
            continue;
        }
        if (n >= 1000000000000ll)
        {
            // if (check(ll(n * 4) - 3))
            // {
            ll delta = 1 - 4 * (1 - n);
            ll x = 0.5 * (-1 + sqrt(delta));
            if (x * x + x + 1 == n)
                cout << "YES"
                     << "\n";
            else
                cout << "NO"
                     << "\n";
            // }
            // else
            // {
            // cout << "NO"
            // << "\n";
            // }
        }
        else
        {
            if (bs(n))
                cout << "YES"
                     << "\n";
            else
                cout << "NO"
                     << "\n";
        }
    }
    return 0;
}

思路，利用等比数列求和公式。在 $10^{12}≤n$ 之前用上面的公式加二分。

在之后用方程 $k^2+k+1=n$验证