public class Solution {
    private int Steps(int x, int y, int mod) {
        var distance = Math.Abs(x - y);
        var coDistance = mod - distance;
        return Math.Min(distance, coDistance);
    }

    private void Relax(string ring, string key, int[][] dp, int r, int k) {
        for (var c = 0; c < ring.Length; ++c) {
            if (ring[c] != key[k]) {
                continue;
            }

            dp[r][k] = Math.Min(
                dp[r][k],
                1 + Steps(r, c, ring.Length) + dp[c][k + 1]
            );
        }
    }

    public int FindRotateSteps(string ring, string key) {
        var dp = new int[ring.Length][];
        for (var i = 0; i < ring.Length; ++i) {
            var ringPosition = new int[key.Length + 1];

            Array.Fill(ringPosition, int.MaxValue);
            ringPosition[key.Length] = 0;

            dp[i] = ringPosition;
        }

        for (var k = key.Length - 1; k >= 0; --k) {
            for (var r = 0; r < ring.Length; ++r) {
                Relax(ring, key, dp, r, k);
            }
        }

        return dp[0][0];
    }
}