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class Solution {
    private Map<Integer, Map<Integer, Integer>> cacheMap;

    public int change(int amount, int[] coins) {
        if (amount == 0) {
            return 1;
        }
        this.cacheMap = new HashMap<>();  // init every time
        Arrays.sort(coins);
        return change(amount, coins, 0);
    }

    public int change(int amount, int[] coins, int fromIdx) {
        if (fromIdx >= coins.length || coins[fromIdx] > amount) {
            return 0;
        }
        Map<Integer, Integer> map = cacheMap.computeIfAbsent(fromIdx, k -> new HashMap<>());
        if (map.containsKey(amount)) {
            return map.get(amount);
        }
        int count = 0;
        int i = 0;
        int base = 0;
        while (base <= amount) {
            if (base == amount) {
                count += 1;
            } else {
                count += change(amount-base, coins, fromIdx+1);
            }
            base += coins[fromIdx];
        }

        map.put(amount, count);
        return count;
    }
}