1. Abridged Problem Statement
Given a positive integer n (up to 10^17), find any permutation of its digits (not starting with zero) that is divisible by 17. If none exists, output −1.

2. Detailed Editorial

We need to reorder the digits of n so that the resulting number is a multiple of 17, with the extra restriction that the number does not begin with '0'. A brute-force over all permutations is O(n!), which is hopeless when n can be up to 17 digits. Instead, we use a bitmask DP with state:

  dp[mask][r] = the minimum integer value (as 64-bit) we can form by using exactly the set of digit-positions in "mask" and achieving a remainder r modulo 17.

Here mask is a subset of {0,…,n−1} indicating which digit positions of the original string s are already used. There are 2^n masks; for each we store 17 remainders, so the total states are 2^n·17 ≤ 131072·17 ≃ 2.2·10^6. Transitions:

  - We iterate masks in increasing order. For each mask, we first count how many of the chosen digits so far are nonzero; call that cnt_non_zero.
  - We try to append each unused position i to the current partial number, but skip if s[i]=='0' and cnt_non_zero==0 (that would make the leading digit zero).
  - If the old remainder is j, appending digit d = s[i]−'0' yields new remainder (10·j + d) mod 17, and new numeric value old_value·10 + d. We minimize dp[mask∪{i}][new_rem].

We initialize dp[0][0] = 0 (empty number, rem=0, value=0) and all other states = +∞. In the end we look at dp[(1<<n)−1][0]: if it is still +∞, answer is −1; otherwise it is the smallest valid rearrangement.

Time Complexity: O(2^n · n · 17) ~ 131072·17·17 ≃ 38·10^6 operations for n up to 17, which fits in 0.25 s in optimized C++.

3. C++ Solution

```cpp
#include <bits/stdc++.h>

using namespace std;

template<typename T1, typename T2>
ostream& operator<<(ostream& out, const pair<T1, T2>& x) {
    return out << x.first << ' ' << x.second;
}

template<typename T1, typename T2>
istream& operator>>(istream& in, pair<T1, T2>& x) {
    return in >> x.first >> x.second;
}

template<typename T>
istream& operator>>(istream& in, vector<T>& a) {
    for(auto& x: a) {
        in >> x;
    }
    return in;
};

template<typename T>
ostream& operator<<(ostream& out, const vector<T>& a) {
    for(auto x: a) {
        out << x << ' ';
    }
    return out;
};

string s;

void read() { cin >> s; }

void solve() {
    // Bitmask DP over which digit positions have already been placed.
    //
    // - dp[mask][r] = the smallest number we can build by placing exactly
    //   the digits in mask, whose value modulo 17 equals r. We extend a
    //   state by appending one not-yet-used digit, keeping the minimal
    //   value so the final answer is the smallest valid permutation.
    //
    // - To avoid a leading zero we forbid placing a '0' as the very first
    //   digit (when no non-zero digit has been placed yet, i.e. the count
    //   of non-zero digits already in mask is 0).
    //
    // - The answer is dp[full][0]; if it stays at infinity no permutation
    //   is divisible by 17 and we print -1.

    if(s == "0") {
        cout << s << '\n';
        return;
    }

    int n = s.size();
    vector<vector<int64_t>> dp(
        1 << n, vector<int64_t>(17, numeric_limits<int64_t>::max())
    );
    dp[0][0] = 0;
    for(int mask = 0; mask < (1 << n); mask++) {
        int cnt_non_zero = 0;
        for(int i = 0; i < n; i++) {
            if((mask & (1 << i)) && s[i] != '0') {
                cnt_non_zero++;
            }
        }

        for(int i = 0; i < n; i++) {
            if((s[i] == '0' && cnt_non_zero == 0) || (mask & (1 << i))) {
                continue;
            }

            for(int j = 0; j < 17; j++) {
                if(dp[mask][j] == numeric_limits<int64_t>::max()) {
                    continue;
                }
                int nmask = mask | (1 << i);
                int nval = (j * 10 + s[i] - '0') % 17;
                dp[nmask][nval] =
                    min(dp[nmask][nval], dp[mask][j] * 10 + s[i] - '0');
            }
        }
    }

    int64_t ans = dp[(1 << n) - 1][0];
    if(ans == numeric_limits<int64_t>::max()) {
        cout << "-1\n";
        return;
    }

    cout << ans << '\n';
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int T = 1;
    // cin >> T;
    for(int test = 1; test <= T; test++) {
        read();
        // cout << "Case #" << test << ": ";
        solve();
    }

    return 0;
}
```

4. Python Solution with Detailed Comments

```python
def find_permutation_div_by_17(s):
    """
    Given a string of digits s, find the minimum permutation
    (no leading zero) divisible by 17, or return '-1'.
    """
    n = len(s)
    # Special case
    if s == "0":
        return "0"

    FULL = 1 << n
    INF = 10**30
    # dp[mask][r] = minimum integer value formed, or INF if impossible
    dp = [ [INF]*17 for _ in range(FULL) ]
    dp[0][0] = 0

    # Precompute digits as ints
    digits = list(map(int, s))

    for mask in range(FULL):
        # Count how many non-zero digits used so far
        cnt_non_zero = 0
        for i in range(n):
            if (mask >> i) & 1 and digits[i] != 0:
                cnt_non_zero += 1

        # Try to add each unused index i next
        for i in range(n):
            if (mask >> i) & 1:
                continue
            d = digits[i]
            # Avoid leading zero if we have not yet placed a non-zero digit
            if d == 0 and cnt_non_zero == 0:
                continue

            new_mask = mask | (1 << i)
            # Go through each old remainder
            for r in range(17):
                old_val = dp[mask][r]
                if old_val == INF:
                    continue
                new_r = (r * 10 + d) % 17
                new_val = old_val * 10 + d
                # Take the minimum numeric value
                if new_val < dp[new_mask][new_r]:
                    dp[new_mask][new_r] = new_val

    ans = dp[FULL - 1][0]
    return str(ans) if ans < INF else "-1"

if __name__ == "__main__":
    s = input().strip()
    print(find_permutation_div_by_17(s))
```

5. Compressed Editorial

Use bitmask DP over subsets of digit positions. dp[mask][r] holds the minimal integer you can build from the digits in mask with remainder r mod 17. Start at dp[0][0]=0; for each mask, count if you already placed a nonzero (to forbid a leading zero), then for every unused position i, transition to mask|{i}, updating remainder (r·10+digit_i)%17 and numeric value old*10+digit_i. Answer is dp[(1<<n)−1][0] or −1 if unreachable. Time: O(2^n · n · 17).
